All problems

Composition of functions 59

13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 13.14 13.15 13.153 13.154 13.155 13.156 13.157 13.158 13.159 13.160 13.161 13.162 13.191 13.192 13.193 13.194 13.195 13.196 13.197 13.198 13.199 13.200 13.201 13.202 13.203 13.204 13.351 13.352 13.353 13.354 13.355 13.356 13.357 13.358 13.359 13.360 13.429 13.430 13.431 13.432 13.433 13.434 13.435 13.436 13.437 13.438

Inverse functions 60

13.31 13.32 13.33 13.34 13.35 13.36 13.37 13.38 13.39 13.40 13.41 13.42 13.43 13.44 13.45 13.163 13.164 13.165 13.166 13.167 13.168 13.169 13.170 13.171 13.172 13.220 13.221 13.222 13.223 13.224 13.225 13.226 13.227 13.228 13.229 13.230 13.231 13.232 13.233 13.234 13.371 13.372 13.373 13.374 13.375 13.376 13.377 13.378 13.379 13.380 13.449 13.450 13.451 13.452 13.453 13.454 13.455 13.456 13.457 13.458

Exact trigonometric values 60

13.46 13.47 13.48 13.49 13.50 13.51 13.52 13.53 13.54 13.55 13.56 13.57 13.58 13.59 13.60 13.235 13.236 13.237 13.238 13.239 13.240 13.241 13.242 13.243 13.244 13.245 13.246 13.247 13.248 13.249 13.332 13.333 13.334 13.335 13.336 13.337 13.338 13.339 13.340 13.341 13.411 13.412 13.413 13.414 13.415 13.416 13.417 13.418 13.419 13.420 13.489 13.490 13.491 13.492 13.493 13.494 13.495 13.496 13.497 13.498

Exact values of inverse trig functions 25

13.61 13.62 13.63 13.64 13.65 13.66 13.67 13.68 13.69 13.70 13.71 13.72 13.73 13.74 13.75 13.173 13.174 13.175 13.176 13.177 13.178 13.179 13.180 13.250 13.311

Solving trigonometric equations 60

13.76 13.77 13.78 13.79 13.80 13.81 13.82 13.83 13.84 13.85 13.86 13.87 13.88 13.89 13.90 13.251 13.252 13.253 13.254 13.255 13.256 13.257 13.258 13.259 13.260 13.261 13.262 13.263 13.264 13.265 13.322 13.323 13.324 13.325 13.326 13.327 13.328 13.329 13.330 13.331 13.401 13.402 13.403 13.404 13.405 13.406 13.407 13.408 13.409 13.410 13.479 13.480 13.481 13.482 13.483 13.484 13.485 13.486 13.487 13.488

Exponential and logarithmic equations 60

13.106 13.107 13.108 13.109 13.110 13.111 13.112 13.113 13.114 13.115 13.116 13.117 13.118 13.119 13.120 13.181 13.182 13.183 13.184 13.185 13.186 13.187 13.188 13.189 13.190 13.281 13.282 13.283 13.284 13.285 13.286 13.287 13.288 13.289 13.290 13.291 13.292 13.293 13.294 13.295 13.381 13.382 13.383 13.384 13.385 13.386 13.387 13.388 13.389 13.390 13.459 13.460 13.461 13.462 13.463 13.464 13.465 13.466 13.467 13.468

Domain of a function 60

13.16 13.17 13.18 13.19 13.20 13.21 13.22 13.23 13.24 13.25 13.26 13.27 13.28 13.29 13.30 13.143 13.144 13.145 13.146 13.147 13.148 13.149 13.150 13.151 13.152 13.205 13.206 13.207 13.208 13.209 13.210 13.211 13.212 13.213 13.214 13.215 13.216 13.217 13.218 13.219 13.361 13.362 13.363 13.364 13.365 13.366 13.367 13.368 13.369 13.370 13.439 13.440 13.441 13.442 13.443 13.444 13.445 13.446 13.447 13.448

Amplitude, period and phase shift 60

13.91 13.92 13.93 13.94 13.95 13.96 13.97 13.98 13.99 13.100 13.101 13.102 13.103 13.104 13.105 13.266 13.267 13.268 13.269 13.270 13.271 13.272 13.273 13.274 13.275 13.276 13.277 13.278 13.279 13.280 13.312 13.313 13.314 13.315 13.316 13.317 13.318 13.319 13.320 13.321 13.391 13.392 13.393 13.394 13.395 13.396 13.397 13.398 13.399 13.400 13.469 13.470 13.471 13.472 13.473 13.474 13.475 13.476 13.477 13.478

Lines and slopes 63

13.121 13.122 13.123 13.124 13.125 13.126 13.127 13.128 13.129 13.130 13.131 13.132 13.133 13.134 13.135 13.136 13.137 13.138 13.139 13.140 13.141 13.142 13.296 13.297 13.298 13.299 13.300 13.301 13.302 13.303 13.304 13.305 13.306 13.307 13.308 13.309 13.310 13.342 13.343 13.344 13.345 13.346 13.347 13.348 13.349 13.350 13.421 13.422 13.423 13.424 13.425 13.426 13.427 13.428 13.499 13.500 13.501 13.502 13.503 13.504 13.505 13.506 13.507

Limits by direct substitution 36

1.3 1.5 1.17 1.20 1.24 1.32 1.36 1.44 1.49 1.50 1.61 1.63 1.73 1.76 1.82 1.86 1.89 1.102 1.108 1.112 1.118 1.121 1.128 1.130 1.135 1.153 1.158 1.161 1.166 1.172 1.174 1.226 1.228 1.233 1.238 1.247

Limits by factoring 63

1.1 1.9 1.11 1.18 1.21 1.25 1.31 1.38 1.41 1.43 1.55 1.58 1.62 1.67 1.84 1.91 1.92 1.96 1.111 1.125 1.133 1.140 1.143 1.146 1.148 1.149 1.162 1.163 1.175 1.219 1.221 1.222 1.230 1.235 1.241 1.259 1.303 1.309 1.310 1.312 1.321 1.324 1.326 1.329 1.363 1.364 1.371 1.372 1.380 1.414 1.454 1.467 1.499 1.558 1.635 1.703 1.717 1.719 1.771 1.772 1.774 1.795 1.811

Limits by rationalizing 45

1.10 1.14 1.23 1.29 1.35 1.40 1.52 1.53 1.68 1.72 1.75 1.78 1.85 1.93 1.97 1.106 1.116 1.119 1.127 1.134 1.137 1.142 1.144 1.159 1.160 1.173 1.178 1.220 1.224 1.236 1.243 1.252 1.301 1.354 1.358 1.359 1.367 1.420 1.421 1.463 1.523 1.557 1.714 1.798 1.799

Trigonometric limits 69

1.6 1.15 1.16 1.26 1.33 1.37 1.46 1.54 1.59 1.64 1.69 1.77 1.80 1.87 1.90 1.99 1.103 1.113 1.117 1.123 1.131 1.136 1.141 1.145 1.150 1.152 1.155 1.156 1.165 1.171 1.225 1.229 1.234 1.239 1.248 1.250 1.251 1.253 1.258 1.305 1.307 1.314 1.315 1.316 1.320 1.322 1.327 1.331 1.355 1.356 1.373 1.377 1.378 1.411 1.413 1.419 1.422 1.425 1.426 1.451 1.457 1.458 1.466 1.498 1.502 1.524 1.556 1.637 1.810

Limits at infinity 62

1.2 1.7 1.19 1.22 1.27 1.30 1.39 1.42 1.45 1.48 1.60 1.65 1.70 1.79 1.95 1.98 1.100 1.104 1.107 1.115 1.124 1.129 1.132 1.138 1.147 1.154 1.157 1.167 1.168 1.177 1.223 1.227 1.242 1.244 1.246 1.249 1.255 1.260 1.302 1.304 1.306 1.318 1.319 1.323 1.325 1.328 1.353 1.365 1.366 1.368 1.369 1.370 1.374 1.379 1.412 1.416 1.417 1.418 1.452 1.459 1.465 1.559

L'Hôpital's rule 76

1.4 1.8 1.12 1.13 1.28 1.34 1.47 1.51 1.56 1.57 1.66 1.71 1.74 1.81 1.83 1.88 1.94 1.101 1.105 1.109 1.110 1.114 1.120 1.122 1.126 1.139 1.151 1.164 1.169 1.170 1.176 1.231 1.232 1.237 1.240 1.245 1.254 1.256 1.257 1.308 1.311 1.313 1.317 1.330 1.332 1.357 1.360 1.361 1.362 1.375 1.376 1.415 1.423 1.424 1.427 1.428 1.429 1.430 1.453 1.455 1.456 1.460 1.461 1.462 1.464 1.500 1.501 1.525 1.636 1.718 1.740 1.750 1.773 1.796 1.797 1.822

Limit laws with given limits 60

1.209 1.210 1.211 1.212 1.213 1.214 1.215 1.216 1.217 1.218 1.333 1.334 1.335 1.336 1.337 1.338 1.339 1.340 1.341 1.342 1.431 1.432 1.433 1.434 1.435 1.436 1.437 1.438 1.439 1.440 1.503 1.504 1.505 1.506 1.507 1.508 1.509 1.510 1.511 1.512 1.560 1.561 1.562 1.563 1.564 1.565 1.566 1.567 1.568 1.569 1.775 1.776 1.777 1.778 1.779 1.780 1.781 1.782 1.783 1.784

One-sided limits of piecewise functions 60

1.261 1.262 1.263 1.264 1.265 1.266 1.267 1.268 1.269 1.270 1.343 1.344 1.345 1.346 1.347 1.348 1.349 1.350 1.351 1.352 1.441 1.442 1.443 1.444 1.445 1.446 1.447 1.448 1.449 1.450 1.513 1.514 1.515 1.516 1.517 1.518 1.519 1.520 1.521 1.522 1.570 1.571 1.572 1.573 1.574 1.575 1.576 1.577 1.578 1.579 1.800 1.801 1.802 1.803 1.804 1.805 1.806 1.807 1.808 1.809

Continuity and types of discontinuity 60

1.189 1.190 1.191 1.192 1.193 1.194 1.195 1.196 1.197 1.198 1.281 1.282 1.283 1.284 1.285 1.286 1.287 1.288 1.289 1.290 1.391 1.392 1.393 1.394 1.395 1.396 1.397 1.398 1.399 1.400 1.478 1.479 1.480 1.481 1.482 1.483 1.484 1.485 1.486 1.487 1.536 1.537 1.538 1.539 1.540 1.541 1.542 1.543 1.544 1.545 1.751 1.752 1.753 1.754 1.755 1.756 1.757 1.758 1.759 1.760

Making a piecewise function continuous 60

1.199 1.200 1.201 1.202 1.203 1.204 1.205 1.206 1.207 1.208 1.291 1.292 1.293 1.294 1.295 1.296 1.297 1.298 1.299 1.300 1.401 1.402 1.403 1.404 1.405 1.406 1.407 1.408 1.409 1.410 1.488 1.489 1.490 1.491 1.492 1.493 1.494 1.495 1.496 1.497 1.546 1.547 1.548 1.549 1.550 1.551 1.552 1.553 1.554 1.555 1.761 1.762 1.763 1.764 1.765 1.766 1.767 1.768 1.769 1.770

Vertical and horizontal asymptotes 60

1.179 1.180 1.181 1.182 1.183 1.184 1.185 1.186 1.187 1.188 1.271 1.272 1.273 1.274 1.275 1.276 1.277 1.278 1.279 1.280 1.381 1.382 1.383 1.384 1.385 1.386 1.387 1.388 1.389 1.390 1.468 1.469 1.470 1.471 1.472 1.473 1.474 1.475 1.476 1.477 1.526 1.527 1.528 1.529 1.530 1.531 1.532 1.533 1.534 1.535 1.580 1.581 1.582 1.583 1.584 1.585 1.586 1.587 1.588 1.589

Estimating a limit from a table 60

1.590 1.591 1.592 1.593 1.594 1.595 1.596 1.597 1.598 1.599 1.600 1.601 1.602 1.603 1.604 1.648 1.649 1.650 1.651 1.652 1.653 1.654 1.655 1.656 1.657 1.658 1.659 1.660 1.661 1.662 1.663 1.664 1.665 1.666 1.667 1.668 1.669 1.670 1.671 1.672 1.720 1.721 1.722 1.723 1.724 1.725 1.726 1.727 1.728 1.729 1.785 1.786 1.787 1.788 1.789 1.790 1.791 1.792 1.793 1.794

Intermediate Value Theorem: locating a root 58

1.605 1.606 1.607 1.608 1.609 1.610 1.611 1.612 1.613 1.614 1.615 1.616 1.617 1.618 1.619 1.638 1.639 1.640 1.641 1.642 1.643 1.644 1.645 1.646 1.647 1.673 1.674 1.675 1.676 1.677 1.678 1.679 1.680 1.681 1.682 1.683 1.684 1.685 1.686 1.687 1.715 1.716 1.741 1.742 1.743 1.744 1.745 1.746 1.747 1.748 1.749 1.823 1.824 1.825 1.826 1.827 1.828 1.829

The squeeze theorem 60

1.620 1.621 1.622 1.623 1.624 1.625 1.626 1.627 1.628 1.629 1.630 1.631 1.632 1.633 1.634 1.688 1.689 1.690 1.691 1.692 1.693 1.694 1.695 1.696 1.697 1.698 1.699 1.700 1.701 1.702 1.704 1.705 1.706 1.707 1.708 1.709 1.710 1.711 1.712 1.713 1.730 1.731 1.732 1.733 1.734 1.735 1.736 1.737 1.738 1.739 1.812 1.813 1.814 1.815 1.816 1.817 1.818 1.819 1.820 1.821

Power rule 313

2.7 2.16 2.37 2.42 2.47 2.50 2.57 2.75 2.86 2.87 2.98 2.100 2.102 2.114 2.141 2.143 2.146 2.151 2.155 2.163 2.169 2.176 2.180 2.198 2.199 2.202 2.208 2.240 2.242 2.244 2.248 2.250 2.256 2.295 2.320 2.374 2.379 2.391 2.430 2.438 2.446 2.452 2.460 2.472 2.513 2.522 2.627 2.636 2.643 2.646 2.667 2.679 2.693 2.697 2.698 2.711 2.716 2.829 2.831 2.879 2.885 2.890 2.979 2.984 2.989 2.997 2.1000 2.1004 2.1008 2.1016 2.1025 2.1026 2.1073 2.1078 2.1085 2.1087 2.1103 2.1105 2.1106 2.1112 2.1130 2.1140 2.1165 2.1180 2.1181 2.1186 2.1203 2.1213 2.1216 2.1218 2.1236 2.1259 2.1293 2.1304 2.1324 2.1329 2.1331 2.1333 2.1339 2.1340 2.1341 2.1343 2.1344 2.1347 2.1355 2.1375 2.1377 2.1379 2.1389 2.1400 2.1405 2.1407 2.1408 2.1410 2.1416 2.1419 2.1486 2.1492 2.1494 2.1500 2.1507 2.1508 2.1511 2.1523 2.1567 2.1569 2.1570 2.1580 2.1581 2.1585 2.1586 2.1588 2.1593 2.1597 2.1603 2.1607 2.1609 2.1610 2.1651 2.1652 2.1653 2.1655 2.1659 2.1667 2.1671 2.1679 2.1680 2.1686 2.1688 2.1695 2.1737 2.1739 2.1744 2.1757 2.1758 2.1759 2.1760 2.1761 2.1764 2.1765 2.1766 2.1770 2.1771 2.1773 2.1775 2.1784 2.1817 2.1822 2.1826 2.1834 2.1835 2.1838 2.1840 2.1841 2.1842 2.1845 2.1846 2.1848 2.1852 2.1855 2.1893 2.1894 2.1897 2.1900 2.1901 2.1902 2.1908 2.1910 2.1921 2.1926 2.1932 2.1933 2.1974 2.1978 2.1981 2.1989 2.1990 2.1992 2.1997 2.2003 2.2005 2.2007 2.2011 2.2014 2.2020 2.2042 2.2044 2.2046 2.2050 2.2051 2.2054 2.2058 2.2061 2.2062 2.2063 2.2066 2.2068 2.2069 2.2071 2.2076 2.2077 2.2078 2.2080 2.2084 2.2085 2.2109 2.2110 2.2111 2.2114 2.2115 2.2117 2.2120 2.2121 2.2123 2.2126 2.2131 2.2133 2.2134 2.2136 2.2138 2.2139 2.2140 2.2141 2.2143 2.2168 2.2169 2.2171 2.2172 2.2173 2.2174 2.2175 2.2177 2.2180 2.2181 2.2188 2.2189 2.2190 2.2192 2.2193 2.2195 2.2197 2.2198 2.2199 2.2200 2.2204 2.2265 2.2268 2.2269 2.2270 2.2273 2.2274 2.2276 2.2277 2.2280 2.2281 2.2284 2.2285 2.2286 2.2287 2.2288 2.2289 2.2291 2.2293 2.2296 2.2297 2.2299 2.2377 2.2380 2.2381 2.2384 2.2386 2.2388 2.2390 2.2391 2.2395 2.2397 2.2402 2.2403 2.2405 2.2406 2.2407 2.2408 2.2409 2.2410 2.2412 2.2416 2.2417 2.2418 2.2421 2.2424 2.2428 2.2439 2.2443

Product rule 264

2.12 2.22 2.30 2.55 2.68 2.78 2.85 2.92 2.96 2.123 2.145 2.201 2.222 2.278 2.310 2.314 2.315 2.316 2.317 2.342 2.384 2.387 2.390 2.397 2.403 2.426 2.428 2.458 2.478 2.498 2.511 2.517 2.520 2.529 2.537 2.539 2.551 2.575 2.584 2.594 2.603 2.609 2.621 2.622 2.632 2.645 2.652 2.653 2.654 2.656 2.658 2.660 2.663 2.668 2.669 2.674 2.676 2.683 2.705 2.710 2.713 2.839 2.840 2.844 2.846 2.860 2.861 2.866 2.869 2.870 2.874 2.883 2.884 2.891 2.895 2.897 2.948 2.951 2.960 2.961 2.964 2.967 2.971 2.982 2.993 2.1014 2.1015 2.1018 2.1020 2.1022 2.1024 2.1027 2.1030 2.1060 2.1061 2.1064 2.1066 2.1067 2.1080 2.1086 2.1091 2.1096 2.1109 2.1114 2.1116 2.1117 2.1127 2.1128 2.1134 2.1136 2.1141 2.1178 2.1183 2.1190 2.1193 2.1198 2.1199 2.1208 2.1212 2.1219 2.1222 2.1223 2.1224 2.1229 2.1238 2.1239 2.1242 2.1244 2.1246 2.1249 2.1281 2.1286 2.1295 2.1297 2.1303 2.1307 2.1310 2.1312 2.1316 2.1319 2.1320 2.1321 2.1327 2.1328 2.1342 2.1348 2.1358 2.1361 2.1372 2.1376 2.1380 2.1381 2.1386 2.1392 2.1402 2.1404 2.1420 2.1421 2.1427 2.1428 2.1429 2.1433 2.1435 2.1443 2.1445 2.1447 2.1489 2.1490 2.1499 2.1512 2.1515 2.1566 2.1572 2.1574 2.1575 2.1577 2.1582 2.1587 2.1589 2.1590 2.1595 2.1599 2.1600 2.1604 2.1660 2.1663 2.1672 2.1673 2.1682 2.1683 2.1684 2.1693 2.1743 2.1748 2.1749 2.1751 2.1756 2.1768 2.1779 2.1781 2.1783 2.1821 2.1824 2.1829 2.1832 2.1839 2.1843 2.1844 2.1856 2.1906 2.1907 2.1909 2.1913 2.1922 2.1923 2.1930 2.1931 2.1935 2.1939 2.1984 2.1985 2.1991 2.1996 2.2012 2.2015 2.2018 2.2019 2.2049 2.2055 2.2057 2.2060 2.2072 2.2074 2.2112 2.2113 2.2119 2.2124 2.2127 2.2128 2.2130 2.2170 2.2178 2.2182 2.2262 2.2278 2.2282 2.2283 2.2376 2.2378 2.2382 2.2383 2.2387 2.2400 2.2414 2.2422 2.2426 2.2427 2.2440 2.2461 2.2462 2.2477 2.2534 2.2555 2.2556

Quotient rule 119

2.322 2.325 2.328 2.330 2.332 2.337 2.339 2.346 2.359 2.362 2.367 2.372 2.409 2.417 2.427 2.436 2.441 2.442 2.443 2.445 2.450 2.457 2.487 2.496 2.504 2.514 2.521 2.540 2.556 2.558 2.564 2.568 2.572 2.576 2.586 2.588 2.589 2.595 2.599 2.615 2.624 2.628 2.642 2.644 2.647 2.661 2.670 2.672 2.677 2.686 2.687 2.694 2.715 2.826 2.828 2.835 2.836 2.847 2.855 2.867 2.872 2.887 2.896 2.902 2.935 2.943 2.949 2.952 2.953 2.973 2.975 2.978 2.987 2.1006 2.1019 2.1023 2.1028 2.1062 2.1088 2.1095 2.1113 2.1124 2.1139 2.1166 2.1172 2.1176 2.1188 2.1211 2.1214 2.1225 2.1228 2.1234 2.1240 2.1247 2.1248 2.1288 2.1290 2.1291 2.1292 2.1296 2.1306 2.1325 2.1354 2.1366 2.1387 2.1413 2.1418 2.1444 2.1452 2.1666 2.1670 2.1689 2.1920 2.1982 2.1993 2.2045 2.2064 2.2184 2.2533

Chain rule 422

2.1 2.2 2.3 2.4 2.5 2.6 2.8 2.9 2.13 2.15 2.17 2.18 2.19 2.20 2.21 2.23 2.24 2.26 2.27 2.28 2.29 2.31 2.32 2.33 2.34 2.35 2.38 2.39 2.41 2.44 2.45 2.48 2.49 2.51 2.52 2.53 2.54 2.56 2.58 2.59 2.61 2.62 2.63 2.64 2.67 2.69 2.70 2.71 2.72 2.73 2.74 2.76 2.77 2.79 2.80 2.81 2.82 2.89 2.90 2.91 2.93 2.94 2.95 2.99 2.104 2.105 2.106 2.109 2.110 2.111 2.113 2.115 2.116 2.117 2.118 2.119 2.120 2.121 2.122 2.124 2.125 2.126 2.128 2.129 2.130 2.131 2.132 2.133 2.134 2.135 2.136 2.137 2.138 2.139 2.140 2.142 2.144 2.148 2.149 2.150 2.152 2.153 2.154 2.157 2.160 2.161 2.162 2.164 2.166 2.167 2.172 2.173 2.174 2.175 2.177 2.178 2.179 2.181 2.182 2.184 2.185 2.186 2.187 2.188 2.190 2.191 2.193 2.194 2.195 2.196 2.197 2.200 2.203 2.205 2.206 2.207 2.209 2.210 2.211 2.212 2.213 2.218 2.219 2.221 2.223 2.224 2.225 2.228 2.229 2.230 2.231 2.232 2.233 2.234 2.235 2.237 2.238 2.239 2.241 2.243 2.246 2.247 2.249 2.251 2.252 2.253 2.254 2.255 2.257 2.258 2.259 2.261 2.262 2.263 2.265 2.266 2.267 2.268 2.269 2.270 2.271 2.272 2.273 2.275 2.276 2.277 2.279 2.280 2.281 2.282 2.283 2.285 2.287 2.288 2.289 2.290 2.291 2.292 2.293 2.294 2.296 2.298 2.300 2.301 2.302 2.303 2.304 2.305 2.306 2.309 2.311 2.312 2.313 2.318 2.319 2.341 2.348 2.351 2.358 2.398 2.399 2.455 2.467 2.469 2.507 2.512 2.525 2.530 2.531 2.532 2.535 2.536 2.541 2.543 2.550 2.552 2.557 2.560 2.563 2.566 2.574 2.598 2.606 2.611 2.619 2.629 2.673 2.675 2.680 2.684 2.691 2.692 2.696 2.700 2.702 2.712 2.718 2.722 2.723 2.724 2.815 2.822 2.824 2.856 2.857 2.862 2.864 2.865 2.878 2.886 2.888 2.889 2.892 2.899 2.900 2.904 2.906 2.907 2.908 2.909 2.910 2.946 2.956 2.969 2.974 2.977 2.995 2.999 2.1017 2.1031 2.1032 2.1033 2.1034 2.1055 2.1056 2.1065 2.1070 2.1071 2.1072 2.1077 2.1079 2.1090 2.1098 2.1100 2.1107 2.1111 2.1122 2.1126 2.1138 2.1143 2.1144 2.1145 2.1168 2.1170 2.1175 2.1177 2.1185 2.1194 2.1201 2.1210 2.1235 2.1237 2.1243 2.1250 2.1257 2.1258 2.1260 2.1262 2.1287 2.1289 2.1294 2.1299 2.1313 2.1336 2.1346 2.1356 2.1357 2.1360 2.1363 2.1364 2.1365 2.1368 2.1369 2.1373 2.1378 2.1388 2.1397 2.1399 2.1401 2.1403 2.1415 2.1423 2.1424 2.1425 2.1430 2.1434 2.1451 2.1453 2.1454 2.1456 2.1476 2.1479 2.1481 2.1493 2.1495 2.1509 2.1513 2.1520 2.1522 2.1565 2.1571 2.1579 2.1584 2.1608 2.1656 2.1658 2.1674 2.1678 2.1692 2.1738 2.1740 2.1745 2.1747 2.1752 2.1753 2.1754 2.1776 2.1816 2.1819 2.1831 2.1833 2.1854 2.1859 2.1891 2.1892 2.1912 2.1918 2.1936 2.1976 2.1979 2.1998 2.1999 2.2002 2.2004 2.2052 2.2056 2.2067 2.2070 2.2081 2.2082 2.2137 2.2145 2.2183 2.2185 2.2191 2.2263 2.2264 2.2271 2.2275 2.2279 2.2379 2.2399

Derivatives of trigonometric functions 233

2.36 2.66 2.101 2.171 2.214 2.297 2.345 2.352 2.360 2.363 2.373 2.383 2.388 2.392 2.393 2.405 2.415 2.423 2.433 2.449 2.454 2.462 2.464 2.468 2.474 2.475 2.479 2.495 2.500 2.501 2.503 2.505 2.523 2.545 2.567 2.573 2.578 2.579 2.580 2.590 2.596 2.601 2.605 2.610 2.623 2.630 2.641 2.659 2.664 2.666 2.671 2.678 2.681 2.688 2.689 2.690 2.699 2.706 2.707 2.708 2.709 2.714 2.833 2.842 2.843 2.845 2.849 2.852 2.853 2.854 2.858 2.859 2.875 2.881 2.882 2.893 2.905 2.950 2.957 2.958 2.959 2.962 2.966 2.972 2.976 2.983 2.986 2.990 2.991 2.992 2.998 2.1002 2.1007 2.1009 2.1010 2.1012 2.1029 2.1076 2.1081 2.1083 2.1084 2.1092 2.1094 2.1108 2.1115 2.1119 2.1123 2.1125 2.1131 2.1132 2.1133 2.1135 2.1137 2.1142 2.1167 2.1169 2.1182 2.1187 2.1189 2.1191 2.1202 2.1215 2.1232 2.1233 2.1255 2.1256 2.1282 2.1283 2.1311 2.1315 2.1317 2.1323 2.1334 2.1349 2.1351 2.1383 2.1409 2.1432 2.1439 2.1480 2.1488 2.1496 2.1497 2.1498 2.1501 2.1503 2.1506 2.1510 2.1514 2.1517 2.1518 2.1519 2.1521 2.1524 2.1576 2.1578 2.1583 2.1592 2.1596 2.1601 2.1602 2.1605 2.1606 2.1654 2.1657 2.1662 2.1664 2.1668 2.1675 2.1676 2.1677 2.1681 2.1685 2.1687 2.1690 2.1694 2.1741 2.1746 2.1755 2.1763 2.1769 2.1774 2.1777 2.1778 2.1780 2.1782 2.1820 2.1823 2.1825 2.1828 2.1830 2.1836 2.1837 2.1847 2.1849 2.1850 2.1851 2.1853 2.1860 2.1861 2.1862 2.1895 2.1896 2.1898 2.1899 2.1903 2.1914 2.1915 2.1916 2.1927 2.1928 2.1934 2.1938 2.1975 2.1977 2.1980 2.1983 2.1988 2.1994 2.2000 2.2013 2.2017 2.2043 2.2047 2.2048 2.2079 2.2167 2.2300 2.2401 2.2420 2.2441 2.2460 2.2474

Derivatives of exponential functions 65

2.25 2.40 2.165 2.274 2.307 2.333 2.336 2.340 2.347 2.361 2.364 2.369 2.381 2.382 2.389 2.394 2.404 2.412 2.413 2.421 2.422 2.432 2.437 2.444 2.451 2.453 2.463 2.471 2.480 2.483 2.488 2.492 2.493 2.506 2.515 2.518 2.524 2.546 2.577 2.582 2.585 2.591 2.593 2.604 2.612 2.616 2.625 2.631 2.638 2.649 2.655 2.685 2.876 2.1093 2.1101 2.1118 2.1179 2.1184 2.1200 2.1284 2.1305 2.1314 2.1322 2.1335 2.1406

Derivatives of logarithms 219

2.10 2.107 2.189 2.215 2.227 2.236 2.286 2.335 2.343 2.354 2.370 2.376 2.395 2.401 2.407 2.416 2.419 2.424 2.429 2.435 2.440 2.447 2.456 2.466 2.476 2.482 2.485 2.491 2.499 2.508 2.509 2.526 2.544 2.561 2.569 2.587 2.600 2.608 2.614 2.618 2.626 2.634 2.640 2.648 2.682 2.695 2.703 2.717 2.719 2.720 2.850 2.851 2.863 2.877 2.880 2.894 2.947 2.955 2.963 2.965 2.985 2.994 2.1001 2.1003 2.1005 2.1021 2.1057 2.1058 2.1063 2.1068 2.1069 2.1074 2.1082 2.1089 2.1099 2.1102 2.1104 2.1110 2.1129 2.1171 2.1173 2.1192 2.1206 2.1207 2.1220 2.1227 2.1230 2.1245 2.1253 2.1254 2.1309 2.1326 2.1332 2.1338 2.1350 2.1362 2.1370 2.1371 2.1374 2.1382 2.1391 2.1393 2.1394 2.1422 2.1431 2.1437 2.1440 2.1442 2.1446 2.1448 2.1450 2.1477 2.1478 2.1482 2.1483 2.1484 2.1487 2.1502 2.1504 2.1505 2.1516 2.1568 2.1573 2.1591 2.1594 2.1598 2.1661 2.1665 2.1669 2.1691 2.1736 2.1742 2.1750 2.1762 2.1767 2.1772 2.1785 2.1818 2.1827 2.1857 2.1858 2.1904 2.1905 2.1911 2.1917 2.1919 2.1924 2.1925 2.1929 2.1937 2.1973 2.1986 2.1987 2.1995 2.2001 2.2006 2.2008 2.2009 2.2010 2.2016 2.2053 2.2059 2.2065 2.2073 2.2075 2.2083 2.2106 2.2107 2.2108 2.2116 2.2118 2.2122 2.2125 2.2129 2.2132 2.2135 2.2142 2.2144 2.2176 2.2179 2.2186 2.2187 2.2194 2.2196 2.2201 2.2202 2.2203 2.2205 2.2206 2.2266 2.2267 2.2272 2.2290 2.2292 2.2294 2.2295 2.2298 2.2385 2.2389 2.2392 2.2393 2.2394 2.2396 2.2398 2.2404 2.2411 2.2413 2.2415 2.2419 2.2423 2.2425 2.2442 2.2473 2.2475 2.2476 2.2478 2.2509 2.2520 2.2521

Derivatives of inverse trig functions 53

2.323 2.326 2.329 2.334 2.353 2.356 2.365 2.375 2.377 2.385 2.400 2.406 2.410 2.414 2.418 2.434 2.439 2.448 2.459 2.465 2.473 2.481 2.484 2.489 2.497 2.548 2.553 2.559 2.565 2.570 2.571 2.583 2.592 2.607 2.617 2.633 2.639 2.650 2.816 2.817 2.820 2.821 2.823 2.827 2.830 2.832 2.838 2.938 2.940 2.942 2.1485 2.1491 2.1890

Logarithmic differentiation 50

2.321 2.324 2.327 2.331 2.338 2.344 2.355 2.357 2.366 2.371 2.378 2.380 2.386 2.396 2.402 2.408 2.420 2.425 2.461 2.470 2.477 2.486 2.490 2.494 2.502 2.510 2.516 2.519 2.527 2.547 2.549 2.554 2.562 2.581 2.597 2.602 2.620 2.635 2.651 2.819 2.825 2.834 2.841 2.936 2.937 2.939 2.941 2.1053 2.1054 2.1280

Tangent lines 70

2.725 2.726 2.727 2.728 2.729 2.730 2.731 2.732 2.733 2.734 2.735 2.736 2.737 2.738 2.739 2.770 2.771 2.772 2.773 2.774 2.775 2.776 2.777 2.778 2.779 2.780 2.781 2.782 2.783 2.784 2.911 2.912 2.913 2.914 2.915 2.916 2.917 2.918 2.1036 2.1037 2.1038 2.1039 2.1040 2.1041 2.1042 2.1043 2.1146 2.1147 2.1148 2.1149 2.1150 2.1151 2.1152 2.1153 2.1263 2.1264 2.1265 2.1266 2.1267 2.1268 2.1269 2.1270 2.1457 2.1458 2.1459 2.1460 2.1461 2.1462 2.1463 2.1464

Second derivatives 47

2.740 2.741 2.742 2.743 2.744 2.745 2.746 2.747 2.748 2.749 2.750 2.751 2.752 2.753 2.754 2.785 2.786 2.787 2.788 2.789 2.790 2.791 2.792 2.793 2.794 2.795 2.796 2.797 2.798 2.799 2.919 2.920 2.921 2.922 2.923 2.924 2.925 2.926 2.1044 2.1154 2.1155 2.1156 2.1271 2.1465 2.1466 2.1467 2.2532

Implicit differentiation 70

2.755 2.756 2.757 2.758 2.759 2.760 2.761 2.762 2.763 2.764 2.765 2.766 2.767 2.768 2.769 2.800 2.801 2.802 2.803 2.804 2.805 2.806 2.807 2.808 2.809 2.810 2.811 2.812 2.813 2.814 2.927 2.928 2.929 2.930 2.931 2.932 2.933 2.934 2.1045 2.1046 2.1047 2.1048 2.1049 2.1050 2.1051 2.1052 2.1157 2.1158 2.1159 2.1160 2.1161 2.1162 2.1163 2.1164 2.1272 2.1273 2.1274 2.1275 2.1276 2.1277 2.1278 2.1279 2.1468 2.1469 2.1470 2.1471 2.1472 2.1473 2.1474 2.1475

The derivative from the limit definition 60

2.1525 2.1526 2.1527 2.1528 2.1529 2.1530 2.1531 2.1532 2.1533 2.1534 2.1631 2.1632 2.1633 2.1634 2.1635 2.1636 2.1637 2.1638 2.1639 2.1640 2.1786 2.1787 2.1788 2.1789 2.1790 2.1791 2.1792 2.1793 2.1794 2.1795 2.1943 2.1944 2.1945 2.1946 2.1947 2.1948 2.1949 2.1950 2.1951 2.1952 2.2086 2.2087 2.2088 2.2089 2.2090 2.2091 2.2092 2.2093 2.2094 2.2095 2.2489 2.2490 2.2491 2.2492 2.2493 2.2494 2.2495 2.2496 2.2497 2.2498

Average rate of change and secant lines 60

2.1621 2.1622 2.1623 2.1624 2.1625 2.1626 2.1627 2.1628 2.1629 2.1630 2.1726 2.1727 2.1728 2.1729 2.1730 2.1731 2.1732 2.1733 2.1734 2.1735 2.1880 2.1881 2.1882 2.1883 2.1884 2.1885 2.1886 2.1887 2.1888 2.1889 2.2032 2.2033 2.2034 2.2035 2.2036 2.2037 2.2038 2.2039 2.2040 2.2041 2.2207 2.2208 2.2209 2.2210 2.2211 2.2212 2.2213 2.2214 2.2215 2.2216 2.2545 2.2546 2.2547 2.2548 2.2549 2.2550 2.2551 2.2552 2.2553 2.2554

Recognising a limit as a derivative 32

2.1555 2.1556 2.1557 2.1558 2.1559 2.1560 2.1561 2.1562 2.1563 2.1564 2.1706 2.1707 2.1708 2.1709 2.1710 2.1711 2.1712 2.1713 2.1714 2.1715 2.1863 2.1864 2.1865 2.1866 2.1867 2.1868 2.1869 2.1940 2.1941 2.1942 2.2021 2.2146

Derivative rules from a table of values 60

2.1535 2.1536 2.1537 2.1538 2.1539 2.1540 2.1541 2.1542 2.1543 2.1544 2.1641 2.1642 2.1643 2.1644 2.1645 2.1646 2.1647 2.1648 2.1649 2.1650 2.1796 2.1797 2.1798 2.1799 2.1800 2.1801 2.1802 2.1803 2.1804 2.1805 2.1953 2.1954 2.1955 2.1956 2.1957 2.1958 2.1959 2.1960 2.1961 2.1962 2.2096 2.2097 2.2098 2.2099 2.2100 2.2101 2.2102 2.2103 2.2104 2.2105 2.2499 2.2500 2.2501 2.2502 2.2503 2.2504 2.2505 2.2506 2.2507 2.2508

Derivative of an inverse function 60

2.1545 2.1546 2.1547 2.1548 2.1549 2.1550 2.1551 2.1552 2.1553 2.1554 2.1696 2.1697 2.1698 2.1699 2.1700 2.1701 2.1702 2.1703 2.1704 2.1705 2.1806 2.1807 2.1808 2.1809 2.1810 2.1811 2.1812 2.1813 2.1814 2.1815 2.1963 2.1964 2.1965 2.1966 2.1967 2.1968 2.1969 2.1970 2.1971 2.1972 2.2147 2.2148 2.2149 2.2150 2.2151 2.2152 2.2153 2.2154 2.2155 2.2156 2.2522 2.2523 2.2524 2.2525 2.2526 2.2527 2.2528 2.2529 2.2530 2.2531

Particle motion: position, velocity, acceleration 60

2.1611 2.1612 2.1613 2.1614 2.1615 2.1616 2.1617 2.1618 2.1619 2.1620 2.1716 2.1717 2.1718 2.1719 2.1720 2.1721 2.1722 2.1723 2.1724 2.1725 2.1870 2.1871 2.1872 2.1873 2.1874 2.1875 2.1876 2.1877 2.1878 2.1879 2.2022 2.2023 2.2024 2.2025 2.2026 2.2027 2.2028 2.2029 2.2030 2.2031 2.2157 2.2158 2.2159 2.2160 2.2161 2.2162 2.2163 2.2164 2.2165 2.2166 2.2535 2.2536 2.2537 2.2538 2.2539 2.2540 2.2541 2.2542 2.2543 2.2544

The chain rule in Leibniz notation 60

2.2217 2.2218 2.2219 2.2220 2.2221 2.2222 2.2223 2.2224 2.2225 2.2226 2.2227 2.2228 2.2229 2.2230 2.2231 2.2301 2.2302 2.2303 2.2304 2.2305 2.2306 2.2307 2.2308 2.2309 2.2310 2.2331 2.2332 2.2333 2.2334 2.2335 2.2336 2.2337 2.2338 2.2339 2.2340 2.2341 2.2342 2.2343 2.2344 2.2345 2.2429 2.2430 2.2431 2.2432 2.2433 2.2434 2.2435 2.2436 2.2437 2.2438 2.2479 2.2480 2.2481 2.2482 2.2483 2.2484 2.2485 2.2486 2.2487 2.2488

Derivatives and integrals of hyperbolic functions 60

2.2232 2.2233 2.2234 2.2235 2.2236 2.2237 2.2238 2.2239 2.2240 2.2241 2.2242 2.2243 2.2244 2.2245 2.2246 2.2311 2.2312 2.2313 2.2314 2.2315 2.2316 2.2317 2.2318 2.2319 2.2320 2.2346 2.2347 2.2348 2.2349 2.2350 2.2351 2.2352 2.2353 2.2354 2.2355 2.2356 2.2357 2.2358 2.2359 2.2360 2.2444 2.2445 2.2446 2.2447 2.2448 2.2449 2.2450 2.2451 2.2452 2.2453 2.2510 2.2511 2.2512 2.2513 2.2514 2.2515 2.2516 2.2517 2.2518 2.2519

Second derivatives by implicit differentiation 56

2.2247 2.2248 2.2249 2.2250 2.2251 2.2252 2.2253 2.2254 2.2255 2.2256 2.2257 2.2258 2.2259 2.2260 2.2261 2.2321 2.2322 2.2323 2.2324 2.2325 2.2326 2.2327 2.2328 2.2329 2.2330 2.2361 2.2362 2.2363 2.2364 2.2365 2.2366 2.2367 2.2368 2.2369 2.2370 2.2371 2.2372 2.2373 2.2374 2.2375 2.2454 2.2455 2.2456 2.2457 2.2458 2.2459 2.2463 2.2464 2.2465 2.2466 2.2467 2.2468 2.2469 2.2470 2.2471 2.2472

Related rates 70

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.91 3.92 3.93 3.94 3.95 3.96 3.97 3.98 3.99 3.100 3.101 3.102 3.103 3.104 3.105 3.175 3.176 3.177 3.178 3.179 3.180 3.181 3.182 3.215 3.216 3.217 3.218 3.219 3.220 3.221 3.222 3.255 3.256 3.257 3.258 3.259 3.260 3.261 3.262 3.295 3.296 3.297 3.298 3.299 3.300 3.301 3.302 3.335 3.336 3.337 3.338 3.339 3.340 3.341 3.342

Linear approximation 70

3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.106 3.107 3.108 3.109 3.110 3.111 3.112 3.113 3.114 3.115 3.116 3.117 3.118 3.119 3.120 3.183 3.184 3.185 3.186 3.187 3.188 3.189 3.190 3.223 3.224 3.225 3.226 3.227 3.228 3.229 3.230 3.263 3.264 3.265 3.266 3.267 3.268 3.269 3.270 3.303 3.304 3.305 3.306 3.307 3.308 3.309 3.310 3.343 3.344 3.345 3.346 3.347 3.348 3.349 3.350

Critical numbers 70

3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 3.44 3.45 3.121 3.122 3.123 3.124 3.125 3.126 3.127 3.128 3.129 3.130 3.131 3.132 3.133 3.134 3.135 3.191 3.192 3.193 3.194 3.195 3.196 3.197 3.198 3.231 3.232 3.233 3.234 3.235 3.236 3.237 3.238 3.271 3.272 3.273 3.274 3.275 3.276 3.277 3.278 3.311 3.312 3.313 3.314 3.315 3.316 3.317 3.318 3.351 3.352 3.353 3.354 3.355 3.356 3.357 3.358

Absolute extrema on a closed interval 70

3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 3.60 3.136 3.137 3.138 3.139 3.140 3.141 3.142 3.143 3.144 3.145 3.146 3.147 3.148 3.149 3.150 3.199 3.200 3.201 3.202 3.203 3.204 3.205 3.206 3.239 3.240 3.241 3.242 3.243 3.244 3.245 3.246 3.279 3.280 3.281 3.282 3.283 3.284 3.285 3.286 3.319 3.320 3.321 3.322 3.323 3.324 3.325 3.326 3.359 3.360 3.361 3.362 3.363 3.364 3.365 3.366

Increasing, decreasing and concavity 70

3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71 3.72 3.73 3.74 3.75 3.151 3.152 3.153 3.154 3.155 3.156 3.157 3.158 3.159 3.160 3.161 3.162 3.163 3.164 3.165 3.207 3.208 3.209 3.210 3.211 3.212 3.213 3.214 3.247 3.248 3.249 3.250 3.251 3.252 3.253 3.254 3.287 3.288 3.289 3.290 3.291 3.292 3.293 3.294 3.327 3.328 3.329 3.330 3.331 3.332 3.333 3.334 3.367 3.368 3.369 3.370 3.371 3.372 3.373 3.374

Optimization 24

3.76 3.77 3.78 3.79 3.80 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89 3.90 3.166 3.167 3.168 3.169 3.170 3.171 3.172 3.173 3.174

Differentials 60

3.385 3.386 3.387 3.388 3.389 3.390 3.391 3.392 3.393 3.394 3.435 3.436 3.437 3.438 3.439 3.440 3.441 3.442 3.443 3.444 3.485 3.486 3.487 3.488 3.489 3.490 3.491 3.492 3.493 3.494 3.535 3.536 3.537 3.538 3.539 3.540 3.541 3.542 3.543 3.544 3.585 3.586 3.587 3.588 3.589 3.590 3.591 3.592 3.593 3.594 3.740 3.741 3.742 3.743 3.744 3.745 3.746 3.747 3.748 3.749

The Mean Value Theorem and Rolle's theorem 60

3.395 3.396 3.397 3.398 3.399 3.400 3.401 3.402 3.403 3.404 3.445 3.446 3.447 3.448 3.449 3.450 3.451 3.452 3.453 3.454 3.495 3.496 3.497 3.498 3.499 3.500 3.501 3.502 3.503 3.504 3.545 3.546 3.547 3.548 3.549 3.550 3.551 3.552 3.553 3.554 3.595 3.596 3.597 3.598 3.599 3.600 3.601 3.602 3.603 3.604 3.760 3.761 3.762 3.763 3.764 3.765 3.766 3.767 3.768 3.769

Newton's method 60

3.405 3.406 3.407 3.408 3.409 3.410 3.411 3.412 3.413 3.414 3.455 3.456 3.457 3.458 3.459 3.460 3.461 3.462 3.463 3.464 3.505 3.506 3.507 3.508 3.509 3.510 3.511 3.512 3.513 3.514 3.555 3.556 3.557 3.558 3.559 3.560 3.561 3.562 3.563 3.564 3.605 3.606 3.607 3.608 3.609 3.610 3.611 3.612 3.613 3.614 3.770 3.771 3.772 3.773 3.774 3.775 3.776 3.777 3.778 3.779

Related rates from an equation 60

3.415 3.416 3.417 3.418 3.419 3.420 3.421 3.422 3.423 3.424 3.465 3.466 3.467 3.468 3.469 3.470 3.471 3.472 3.473 3.474 3.515 3.516 3.517 3.518 3.519 3.520 3.521 3.522 3.523 3.524 3.565 3.566 3.567 3.568 3.569 3.570 3.571 3.572 3.573 3.574 3.615 3.616 3.617 3.618 3.619 3.620 3.621 3.622 3.623 3.624 3.780 3.781 3.782 3.783 3.784 3.785 3.786 3.787 3.788 3.789

Antiderivatives with initial conditions 60

3.375 3.376 3.377 3.378 3.379 3.380 3.381 3.382 3.383 3.384 3.425 3.426 3.427 3.428 3.429 3.430 3.431 3.432 3.433 3.434 3.475 3.476 3.477 3.478 3.479 3.480 3.481 3.482 3.483 3.484 3.525 3.526 3.527 3.528 3.529 3.530 3.531 3.532 3.533 3.534 3.575 3.576 3.577 3.578 3.579 3.580 3.581 3.582 3.583 3.584 3.625 3.626 3.627 3.628 3.629 3.630 3.631 3.632 3.633 3.634

The secant method 30

3.635 3.636 3.637 3.638 3.639 3.640 3.641 3.642 3.643 3.644 3.645 3.646 3.647 3.648 3.649 3.700 3.701 3.702 3.703 3.704 3.720 3.721 3.722 3.723 3.724 3.725 3.726 3.727 3.728 3.739

Business applications: cost, revenue and profit 60

3.650 3.651 3.652 3.653 3.654 3.655 3.656 3.657 3.658 3.659 3.660 3.661 3.662 3.663 3.664 3.680 3.681 3.682 3.683 3.684 3.685 3.686 3.687 3.688 3.689 3.705 3.706 3.707 3.708 3.709 3.710 3.711 3.712 3.713 3.714 3.715 3.716 3.717 3.718 3.719 3.729 3.730 3.731 3.732 3.733 3.734 3.735 3.736 3.737 3.738 3.750 3.751 3.752 3.753 3.754 3.755 3.756 3.757 3.758 3.759

Classic optimization: wire, window, fence 25

3.665 3.666 3.667 3.668 3.669 3.670 3.671 3.672 3.673 3.674 3.675 3.676 3.677 3.678 3.679 3.690 3.691 3.692 3.693 3.694 3.695 3.696 3.697 3.698 3.699

Basic antiderivatives 82

4.170 4.173 4.175 4.176 4.186 4.187 4.193 4.195 4.196 4.198 4.218 4.221 4.226 4.232 4.235 4.252 4.256 4.261 4.263 4.265 4.267 4.270 4.271 4.275 4.279 4.354 4.360 4.361 4.367 4.371 4.373 4.376 4.378 4.469 4.472 4.473 4.477 4.479 4.552 4.555 4.556 4.557 4.649 4.650 4.652 4.654 4.655 4.657 4.661 4.662 4.797 4.799 4.870 4.871 4.874 4.875 4.879 4.882 4.884 4.916 4.921 4.925 4.927 4.1125 4.1212 4.1214 4.1218 4.1219 4.1266 4.1278 4.1279 4.1280 4.1286 4.1287 4.1318 4.1336 4.1405 4.1409 4.1426 4.1428 4.1490 4.1492

u-substitution 93

4.172 4.180 4.181 4.183 4.188 4.189 4.194 4.217 4.225 4.230 4.234 4.253 4.257 4.260 4.262 4.266 4.272 4.280 4.355 4.363 4.369 4.461 4.463 4.464 4.466 4.559 4.562 4.645 4.648 4.658 4.659 4.663 4.728 4.730 4.733 4.734 4.735 4.738 4.740 4.741 4.798 4.802 4.877 4.878 4.880 4.919 4.923 4.924 4.931 4.994 4.995 4.996 4.998 4.1000 4.1001 4.1120 4.1121 4.1122 4.1123 4.1127 4.1128 4.1129 4.1217 4.1220 4.1241 4.1243 4.1245 4.1249 4.1261 4.1265 4.1298 4.1299 4.1310 4.1317 4.1334 4.1335 4.1338 4.1339 4.1341 4.1354 4.1355 4.1401 4.1406 4.1408 4.1427 4.1429 4.1441 4.1443 4.1464 4.1480 4.1482 4.1493 4.1497

Definite integrals 70

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.46 4.47 4.48 4.49 4.50 4.51 4.52 4.53 4.54 4.55 4.56 4.57 4.58 4.59 4.60 4.88 4.89 4.90 4.91 4.92 4.93 4.94 4.95 4.104 4.105 4.106 4.107 4.108 4.109 4.110 4.111 4.121 4.122 4.123 4.124 4.125 4.126 4.127 4.128 4.199 4.200 4.201 4.202 4.203 4.204 4.205 4.206 4.236 4.237 4.238 4.239 4.240 4.241 4.242 4.243

Fundamental Theorem of Calculus, Part 1 70

4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30 4.61 4.62 4.63 4.64 4.65 4.66 4.67 4.68 4.69 4.70 4.71 4.72 4.73 4.74 4.75 4.96 4.97 4.98 4.99 4.100 4.101 4.102 4.103 4.112 4.113 4.114 4.115 4.116 4.117 4.118 4.119 4.129 4.130 4.131 4.132 4.133 4.134 4.135 4.136 4.207 4.208 4.209 4.210 4.211 4.212 4.213 4.214 4.244 4.245 4.246 4.247 4.248 4.249 4.250 4.251

Riemann sums: left, right and midpoint 60

4.400 4.401 4.402 4.403 4.404 4.405 4.406 4.407 4.408 4.409 4.541 4.542 4.543 4.544 4.545 4.546 4.547 4.548 4.549 4.550 4.695 4.696 4.697 4.698 4.699 4.700 4.701 4.702 4.703 4.704 4.846 4.847 4.848 4.849 4.850 4.851 4.852 4.853 4.854 4.855 4.1002 4.1003 4.1004 4.1005 4.1006 4.1007 4.1008 4.1009 4.1010 4.1011 4.1454 4.1455 4.1456 4.1457 4.1458 4.1459 4.1460 4.1461 4.1462 4.1463

Properties of definite integrals 60

4.322 4.323 4.324 4.325 4.326 4.327 4.328 4.329 4.330 4.331 4.491 4.492 4.493 4.494 4.495 4.496 4.497 4.498 4.499 4.500 4.623 4.624 4.625 4.626 4.627 4.628 4.629 4.630 4.631 4.632 4.782 4.783 4.784 4.785 4.786 4.787 4.788 4.789 4.790 4.791 4.943 4.944 4.945 4.946 4.947 4.948 4.949 4.950 4.951 4.952 4.1377 4.1378 4.1379 4.1380 4.1381 4.1382 4.1383 4.1384 4.1385 4.1386

Average value of a function 60

4.292 4.293 4.294 4.295 4.296 4.297 4.298 4.299 4.300 4.301 4.440 4.441 4.442 4.443 4.444 4.445 4.446 4.447 4.448 4.449 4.593 4.594 4.595 4.596 4.597 4.598 4.599 4.600 4.601 4.602 4.752 4.753 4.754 4.755 4.756 4.757 4.758 4.759 4.760 4.761 4.896 4.897 4.898 4.899 4.900 4.901 4.902 4.903 4.904 4.905 4.1323 4.1324 4.1325 4.1326 4.1327 4.1328 4.1329 4.1330 4.1331 4.1332

Integrals of absolute values 60

4.282 4.283 4.284 4.285 4.286 4.287 4.288 4.289 4.290 4.291 4.430 4.431 4.432 4.433 4.434 4.435 4.436 4.437 4.438 4.439 4.583 4.584 4.585 4.586 4.587 4.588 4.589 4.590 4.591 4.592 4.742 4.743 4.744 4.745 4.746 4.747 4.748 4.749 4.750 4.751 4.886 4.887 4.888 4.889 4.890 4.891 4.892 4.893 4.894 4.895 4.1022 4.1023 4.1024 4.1025 4.1026 4.1027 4.1028 4.1029 4.1030 4.1031

Substitution with a given u 60

4.312 4.313 4.314 4.315 4.316 4.317 4.318 4.319 4.320 4.321 4.481 4.482 4.483 4.484 4.485 4.486 4.487 4.488 4.489 4.490 4.613 4.614 4.615 4.616 4.617 4.618 4.619 4.620 4.621 4.622 4.772 4.773 4.774 4.775 4.776 4.777 4.778 4.779 4.780 4.781 4.933 4.934 4.935 4.936 4.937 4.938 4.939 4.940 4.941 4.942 4.1357 4.1358 4.1359 4.1360 4.1361 4.1362 4.1363 4.1364 4.1365 4.1366

Definite integrals by substitution 60

4.302 4.303 4.304 4.305 4.306 4.307 4.308 4.309 4.310 4.311 4.450 4.451 4.452 4.453 4.454 4.455 4.456 4.457 4.458 4.459 4.603 4.604 4.605 4.606 4.607 4.608 4.609 4.610 4.611 4.612 4.762 4.763 4.764 4.765 4.766 4.767 4.768 4.769 4.770 4.771 4.906 4.907 4.908 4.909 4.910 4.911 4.912 4.913 4.914 4.915 4.1342 4.1343 4.1344 4.1345 4.1346 4.1347 4.1348 4.1349 4.1350 4.1351

Integrals giving inverse trig functions 60

4.332 4.333 4.334 4.335 4.336 4.337 4.338 4.339 4.340 4.341 4.501 4.502 4.503 4.504 4.505 4.506 4.507 4.508 4.509 4.510 4.633 4.634 4.635 4.636 4.637 4.638 4.639 4.640 4.641 4.642 4.806 4.807 4.808 4.809 4.810 4.811 4.812 4.813 4.814 4.815 4.953 4.954 4.955 4.956 4.957 4.958 4.959 4.960 4.961 4.962 4.1389 4.1390 4.1391 4.1392 4.1393 4.1394 4.1395 4.1396 4.1397 4.1398

Net change and accumulation from a rate 60

4.342 4.343 4.344 4.345 4.346 4.347 4.348 4.349 4.350 4.351 4.511 4.512 4.513 4.514 4.515 4.516 4.517 4.518 4.519 4.520 4.665 4.666 4.667 4.668 4.669 4.670 4.671 4.672 4.673 4.674 4.816 4.817 4.818 4.819 4.820 4.821 4.822 4.823 4.824 4.825 4.963 4.964 4.965 4.966 4.967 4.968 4.969 4.970 4.971 4.972 4.1410 4.1411 4.1412 4.1413 4.1414 4.1415 4.1416 4.1417 4.1418 4.1419

Sums with sigma notation 60

4.1032 4.1033 4.1034 4.1035 4.1036 4.1037 4.1038 4.1039 4.1040 4.1041 4.1042 4.1043 4.1044 4.1045 4.1046 4.1152 4.1153 4.1154 4.1155 4.1156 4.1157 4.1158 4.1159 4.1160 4.1161 4.1162 4.1163 4.1164 4.1165 4.1166 4.1231 4.1232 4.1233 4.1234 4.1235 4.1236 4.1237 4.1238 4.1239 4.1240 4.1300 4.1301 4.1302 4.1303 4.1304 4.1305 4.1306 4.1307 4.1308 4.1309 4.1465 4.1466 4.1467 4.1468 4.1469 4.1470 4.1471 4.1472 4.1473 4.1474

Limits of Riemann sums as integrals 60

4.1047 4.1048 4.1049 4.1050 4.1051 4.1052 4.1053 4.1054 4.1055 4.1056 4.1057 4.1058 4.1059 4.1060 4.1061 4.1167 4.1168 4.1169 4.1170 4.1171 4.1172 4.1173 4.1174 4.1175 4.1176 4.1177 4.1178 4.1179 4.1180 4.1181 4.1221 4.1222 4.1223 4.1224 4.1225 4.1226 4.1227 4.1228 4.1229 4.1230 4.1288 4.1289 4.1290 4.1291 4.1292 4.1293 4.1294 4.1295 4.1296 4.1297 4.1444 4.1445 4.1446 4.1447 4.1448 4.1449 4.1450 4.1451 4.1452 4.1453

Definite integrals from area formulas 60

4.1062 4.1063 4.1064 4.1065 4.1066 4.1067 4.1068 4.1069 4.1070 4.1071 4.1072 4.1073 4.1074 4.1075 4.1076 4.1140 4.1141 4.1142 4.1143 4.1144 4.1145 4.1146 4.1147 4.1148 4.1149 4.1182 4.1183 4.1184 4.1185 4.1186 4.1187 4.1188 4.1189 4.1190 4.1191 4.1192 4.1193 4.1194 4.1195 4.1196 4.1268 4.1269 4.1270 4.1271 4.1272 4.1273 4.1274 4.1275 4.1276 4.1277 4.1367 4.1368 4.1369 4.1370 4.1371 4.1372 4.1373 4.1374 4.1375 4.1376

Accumulation functions 54

4.1077 4.1078 4.1079 4.1080 4.1081 4.1082 4.1083 4.1084 4.1085 4.1086 4.1087 4.1088 4.1089 4.1090 4.1091 4.1130 4.1131 4.1132 4.1133 4.1134 4.1135 4.1136 4.1137 4.1138 4.1139 4.1197 4.1198 4.1199 4.1200 4.1201 4.1202 4.1203 4.1204 4.1205 4.1206 4.1207 4.1251 4.1252 4.1253 4.1254 4.1255 4.1256 4.1257 4.1258 4.1259 4.1260 4.1313 4.1314 4.1315 4.1316 4.1388 4.1494 4.1495 4.1498

Area between curves 70

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.61 5.62 5.63 5.64 5.65 5.66 5.67 5.68 5.69 5.70 5.71 5.72 5.73 5.74 5.75 5.94 5.95 5.96 5.97 5.98 5.99 5.100 5.101 5.118 5.119 5.120 5.121 5.122 5.123 5.124 5.125 5.142 5.143 5.144 5.145 5.146 5.147 5.148 5.149 5.166 5.167 5.168 5.169 5.170 5.171 5.172 5.173 5.190 5.191 5.192 5.193 5.194 5.195 5.196 5.197

Volumes by disks and washers 18

5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.30 5.76 5.77 5.93

Volumes by cylindrical shells 63

5.31 5.32 5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.40 5.41 5.42 5.43 5.44 5.45 5.78 5.79 5.80 5.81 5.82 5.83 5.84 5.85 5.86 5.87 5.88 5.89 5.90 5.91 5.92 5.102 5.103 5.104 5.105 5.106 5.107 5.108 5.109 5.126 5.127 5.128 5.129 5.130 5.131 5.132 5.133 5.150 5.151 5.152 5.153 5.154 5.155 5.156 5.157 5.174 5.175 5.176 5.177 5.178 5.179 5.180 5.181 5.198

Arc length 57

5.46 5.47 5.48 5.49 5.50 5.51 5.52 5.53 5.54 5.55 5.56 5.57 5.58 5.59 5.60 5.110 5.111 5.112 5.113 5.114 5.115 5.116 5.117 5.134 5.135 5.136 5.137 5.138 5.139 5.140 5.141 5.158 5.159 5.160 5.161 5.162 5.163 5.164 5.165 5.182 5.183 5.184 5.185 5.186 5.187 5.188 5.189 5.199 5.200 5.201 5.202 5.813 5.814 5.815 5.816 5.817 5.818

Volumes with known cross sections 60

5.253 5.254 5.255 5.256 5.257 5.258 5.259 5.260 5.261 5.262 5.323 5.324 5.325 5.326 5.327 5.328 5.329 5.330 5.331 5.332 5.393 5.394 5.395 5.396 5.397 5.398 5.399 5.400 5.401 5.402 5.463 5.464 5.465 5.466 5.467 5.468 5.469 5.470 5.471 5.472 5.533 5.534 5.535 5.536 5.537 5.538 5.539 5.540 5.541 5.542 5.793 5.794 5.795 5.796 5.797 5.798 5.799 5.800 5.801 5.802

Exponential growth and decay 60

5.213 5.214 5.215 5.216 5.217 5.218 5.219 5.220 5.221 5.222 5.283 5.284 5.285 5.286 5.287 5.288 5.289 5.290 5.291 5.292 5.353 5.354 5.355 5.356 5.357 5.358 5.359 5.360 5.361 5.362 5.423 5.424 5.425 5.426 5.427 5.428 5.429 5.430 5.431 5.432 5.493 5.494 5.495 5.496 5.497 5.498 5.499 5.500 5.501 5.502 5.733 5.734 5.735 5.736 5.737 5.738 5.739 5.740 5.741 5.742

Area between curves, integrating in y 10

5.553 5.554 5.555 5.556 5.557 5.558 5.559 5.560 5.561 5.682

Arc length of x = g(y) 60

5.562 5.563 5.564 5.565 5.566 5.567 5.568 5.569 5.570 5.571 5.572 5.573 5.574 5.575 5.576 5.607 5.608 5.609 5.610 5.611 5.612 5.613 5.614 5.615 5.616 5.627 5.628 5.629 5.630 5.631 5.632 5.633 5.634 5.635 5.636 5.637 5.638 5.639 5.640 5.641 5.683 5.684 5.685 5.686 5.687 5.688 5.689 5.690 5.691 5.692 5.713 5.714 5.715 5.716 5.717 5.718 5.719 5.720 5.721 5.722

Integration by parts 90

4.137 4.138 4.139 4.140 4.141 4.142 4.143 4.144 4.145 4.146 4.147 4.148 4.149 4.150 4.151 4.152 4.153 4.154 4.155 4.156 4.157 4.158 4.159 4.160 4.161 4.162 4.163 4.164 4.165 4.166 4.167 4.168 4.169 4.254 4.278 4.356 4.359 4.365 4.370 4.468 4.470 4.560 4.651 4.656 4.660 4.664 4.725 4.726 4.729 4.731 4.732 4.737 4.796 4.801 4.804 4.873 4.876 4.883 4.918 4.922 4.929 4.930 4.993 4.999 4.1124 4.1215 4.1246 4.1248 4.1262 4.1263 4.1282 4.1283 4.1284 4.1311 4.1312 4.1320 4.1321 4.1333 4.1340 4.1353 4.1387 4.1399 4.1400 4.1404 4.1407 4.1440 4.1442 4.1475 4.1478 4.1496

Trigonometric integrals 49

4.174 4.177 4.178 4.182 4.184 4.190 4.192 4.197 4.219 4.222 4.223 4.224 4.228 4.233 4.255 4.258 4.269 4.273 4.274 4.277 4.281 4.357 4.358 4.362 4.366 4.374 4.375 4.377 4.379 4.465 4.467 4.474 4.475 4.476 4.478 4.480 4.554 4.561 4.647 4.653 4.793 4.917 4.920 4.932 4.1126 4.1242 4.1264 4.1356 4.1477

Partial fractions 59

4.171 4.179 4.185 4.191 4.215 4.216 4.220 4.227 4.229 4.231 4.259 4.264 4.268 4.276 4.352 4.353 4.364 4.368 4.372 4.460 4.462 4.471 4.551 4.553 4.558 4.643 4.644 4.646 4.727 4.736 4.739 4.792 4.794 4.795 4.800 4.803 4.805 4.872 4.881 4.926 4.928 4.997 4.1213 4.1216 4.1244 4.1247 4.1267 4.1281 4.1285 4.1319 4.1322 4.1337 4.1352 4.1402 4.1403 4.1476 4.1479 4.1481 4.1491

Improper integrals 28

4.31 4.32 4.33 4.34 4.35 4.36 4.37 4.38 4.39 4.40 4.41 4.42 4.43 4.44 4.45 4.76 4.77 4.78 4.79 4.80 4.81 4.82 4.83 4.84 4.85 4.86 4.87 4.120

Trapezoidal, midpoint and Simpson's rules 56

4.380 4.381 4.382 4.383 4.384 4.385 4.386 4.387 4.388 4.389 4.521 4.522 4.523 4.524 4.525 4.526 4.527 4.528 4.529 4.530 4.675 4.676 4.677 4.678 4.679 4.680 4.681 4.682 4.683 4.684 4.826 4.827 4.828 4.829 4.830 4.831 4.832 4.833 4.834 4.835 4.973 4.974 4.975 4.976 4.977 4.978 4.979 4.980 4.981 4.982 4.1420 4.1421 4.1422 4.1423 4.1424 4.1425

Partial fraction decomposition 60

4.390 4.391 4.392 4.393 4.394 4.395 4.396 4.397 4.398 4.399 4.531 4.532 4.533 4.534 4.535 4.536 4.537 4.538 4.539 4.540 4.685 4.686 4.687 4.688 4.689 4.690 4.691 4.692 4.693 4.694 4.836 4.837 4.838 4.839 4.840 4.841 4.842 4.843 4.844 4.845 4.983 4.984 4.985 4.986 4.987 4.988 4.989 4.990 4.991 4.992 4.1430 4.1431 4.1432 4.1433 4.1434 4.1435 4.1436 4.1437 4.1438 4.1439

Integrals of powers of sine and cosine 57

4.410 4.411 4.412 4.413 4.414 4.415 4.416 4.417 4.418 4.419 4.563 4.564 4.565 4.566 4.567 4.568 4.569 4.570 4.571 4.572 4.705 4.706 4.707 4.708 4.709 4.710 4.711 4.712 4.713 4.714 4.856 4.857 4.858 4.859 4.860 4.861 4.862 4.863 4.864 4.865 4.1012 4.1013 4.1014 4.1015 4.1016 4.1017 4.1018 4.1019 4.1020 4.1021 4.1483 4.1484 4.1485 4.1486 4.1487 4.1488 4.1489

Trigonometric substitution 35

4.420 4.421 4.422 4.423 4.424 4.425 4.426 4.427 4.428 4.429 4.573 4.574 4.575 4.576 4.577 4.578 4.579 4.580 4.581 4.582 4.715 4.716 4.717 4.718 4.719 4.720 4.721 4.722 4.723 4.724 4.866 4.867 4.868 4.869 4.885

Comparison test for improper integrals 13

4.1092 4.1093 4.1094 4.1095 4.1096 4.1097 4.1098 4.1099 4.1100 4.1101 4.1102 4.1103 4.1104

Laplace transforms from the definition 22

4.1105 4.1106 4.1107 4.1108 4.1109 4.1110 4.1111 4.1112 4.1113 4.1114 4.1115 4.1116 4.1117 4.1118 4.1119 4.1150 4.1151 4.1208 4.1209 4.1210 4.1211 4.1250

Separable differential equations 70

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.46 6.47 6.48 6.49 6.50 6.51 6.52 6.53 6.54 6.55 6.56 6.57 6.58 6.59 6.60 6.91 6.92 6.93 6.94 6.95 6.96 6.97 6.98 6.115 6.116 6.117 6.118 6.119 6.120 6.121 6.122 6.139 6.140 6.141 6.142 6.143 6.144 6.145 6.146 6.163 6.164 6.165 6.166 6.167 6.168 6.169 6.170 6.187 6.188 6.189 6.190 6.191 6.192 6.193 6.194

First-order linear equations 70

6.16 6.17 6.18 6.19 6.20 6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28 6.29 6.30 6.61 6.62 6.63 6.64 6.65 6.66 6.67 6.68 6.69 6.70 6.71 6.72 6.73 6.74 6.75 6.99 6.100 6.101 6.102 6.103 6.104 6.105 6.106 6.123 6.124 6.125 6.126 6.127 6.128 6.129 6.130 6.147 6.148 6.149 6.150 6.151 6.152 6.153 6.154 6.171 6.172 6.173 6.174 6.175 6.176 6.177 6.178 6.195 6.196 6.197 6.198 6.199 6.200 6.201 6.202

Euler's method 60

6.211 6.212 6.213 6.214 6.215 6.216 6.217 6.218 6.219 6.220 6.251 6.252 6.253 6.254 6.255 6.256 6.257 6.258 6.259 6.260 6.291 6.292 6.293 6.294 6.295 6.296 6.297 6.298 6.299 6.300 6.331 6.332 6.333 6.334 6.335 6.336 6.337 6.338 6.339 6.340 6.371 6.372 6.373 6.374 6.375 6.376 6.377 6.378 6.379 6.380 6.749 6.750 6.751 6.752 6.753 6.754 6.755 6.756 6.757 6.758

The logistic equation 60

6.221 6.222 6.223 6.224 6.225 6.226 6.227 6.228 6.229 6.230 6.261 6.262 6.263 6.264 6.265 6.266 6.267 6.268 6.269 6.270 6.301 6.302 6.303 6.304 6.305 6.306 6.307 6.308 6.309 6.310 6.341 6.342 6.343 6.344 6.345 6.346 6.347 6.348 6.349 6.350 6.381 6.382 6.383 6.384 6.385 6.386 6.387 6.388 6.389 6.390 6.769 6.770 6.771 6.772 6.773 6.774 6.775 6.776 6.777 6.778

Newton's law of cooling 60

6.231 6.232 6.233 6.234 6.235 6.236 6.237 6.238 6.239 6.240 6.271 6.272 6.273 6.274 6.275 6.276 6.277 6.278 6.279 6.280 6.311 6.312 6.313 6.314 6.315 6.316 6.317 6.318 6.319 6.320 6.351 6.352 6.353 6.354 6.355 6.356 6.357 6.358 6.359 6.360 6.391 6.392 6.393 6.394 6.395 6.396 6.397 6.398 6.399 6.400 6.789 6.790 6.791 6.792 6.793 6.794 6.795 6.796 6.797 6.798

Order and linearity of differential equations 60

6.411 6.412 6.413 6.414 6.415 6.416 6.417 6.418 6.419 6.420 6.421 6.422 6.423 6.424 6.425 6.516 6.517 6.518 6.519 6.520 6.521 6.522 6.523 6.524 6.525 6.556 6.557 6.558 6.559 6.560 6.561 6.562 6.563 6.564 6.565 6.566 6.567 6.568 6.569 6.570 6.669 6.670 6.671 6.672 6.673 6.674 6.675 6.676 6.677 6.678 6.729 6.730 6.731 6.732 6.733 6.734 6.735 6.736 6.737 6.738

Differential equations by direct integration 60

6.426 6.427 6.428 6.429 6.430 6.431 6.432 6.433 6.434 6.435 6.436 6.437 6.438 6.439 6.440 6.526 6.527 6.528 6.529 6.530 6.531 6.532 6.533 6.534 6.535 6.571 6.572 6.573 6.574 6.575 6.576 6.577 6.578 6.579 6.580 6.581 6.582 6.583 6.584 6.585 6.679 6.680 6.681 6.682 6.683 6.684 6.685 6.686 6.687 6.688 6.739 6.740 6.741 6.742 6.743 6.744 6.745 6.746 6.747 6.748

Mixing tank problems 60

6.441 6.442 6.443 6.444 6.445 6.446 6.447 6.448 6.449 6.450 6.451 6.452 6.453 6.454 6.455 6.546 6.547 6.548 6.549 6.550 6.551 6.552 6.553 6.554 6.555 6.586 6.587 6.588 6.589 6.590 6.591 6.592 6.593 6.594 6.595 6.596 6.597 6.598 6.599 6.600 6.699 6.700 6.701 6.702 6.703 6.704 6.705 6.706 6.707 6.708 6.779 6.780 6.781 6.782 6.783 6.784 6.785 6.786 6.787 6.788

Initial-value problems needing partial fractions 60

6.456 6.457 6.458 6.459 6.460 6.461 6.462 6.463 6.464 6.465 6.466 6.467 6.468 6.469 6.470 6.536 6.537 6.538 6.539 6.540 6.541 6.542 6.543 6.544 6.545 6.601 6.602 6.603 6.604 6.605 6.606 6.607 6.608 6.609 6.610 6.611 6.612 6.613 6.614 6.615 6.689 6.690 6.691 6.692 6.693 6.694 6.695 6.696 6.697 6.698 6.759 6.760 6.761 6.762 6.763 6.764 6.765 6.766 6.767 6.768

Geometric series 70

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.61 7.62 7.63 7.64 7.65 7.66 7.67 7.68 7.69 7.70 7.71 7.72 7.73 7.74 7.75 7.121 7.122 7.123 7.124 7.125 7.126 7.127 7.128 7.147 7.148 7.149 7.150 7.151 7.152 7.153 7.154 7.171 7.172 7.173 7.174 7.175 7.176 7.177 7.178 7.195 7.196 7.197 7.198 7.199 7.200 7.201 7.202 7.217 7.218 7.219 7.220 7.221 7.222 7.223 7.224

Series convergence tests 66

7.16 7.17 7.18 7.19 7.20 7.21 7.22 7.23 7.24 7.25 7.26 7.27 7.28 7.29 7.30 7.76 7.77 7.78 7.79 7.80 7.81 7.82 7.83 7.84 7.85 7.86 7.87 7.88 7.89 7.90 7.129 7.130 7.131 7.132 7.133 7.134 7.135 7.136 7.155 7.156 7.157 7.158 7.159 7.160 7.161 7.162 7.179 7.180 7.181 7.182 7.183 7.184 7.185 7.186 7.203 7.204 7.205 7.206 7.207 7.208 7.225 7.226 7.227 7.228 7.229 7.230

Radius of convergence 70

7.46 7.47 7.48 7.49 7.50 7.51 7.52 7.53 7.54 7.55 7.56 7.57 7.58 7.59 7.60 7.106 7.107 7.108 7.109 7.110 7.111 7.112 7.113 7.114 7.115 7.116 7.117 7.118 7.119 7.120 7.139 7.140 7.141 7.142 7.143 7.144 7.145 7.146 7.163 7.164 7.165 7.166 7.167 7.168 7.169 7.170 7.187 7.188 7.189 7.190 7.191 7.192 7.193 7.194 7.209 7.210 7.211 7.212 7.213 7.214 7.215 7.216 7.231 7.232 7.233 7.234 7.235 7.236 7.237 7.238

Taylor and Maclaurin polynomials 32

7.31 7.32 7.33 7.34 7.35 7.36 7.37 7.38 7.39 7.40 7.41 7.42 7.43 7.44 7.45 7.91 7.92 7.93 7.94 7.95 7.96 7.97 7.98 7.99 7.100 7.101 7.102 7.103 7.104 7.105 7.137 7.138

Limits of sequences 61

7.289 7.290 7.291 7.292 7.293 7.294 7.295 7.296 7.297 7.298 7.373 7.374 7.375 7.376 7.377 7.378 7.379 7.380 7.381 7.382 7.437 7.438 7.439 7.440 7.441 7.442 7.443 7.444 7.445 7.457 7.458 7.459 7.500 7.501 7.502 7.503 7.504 7.505 7.506 7.507 7.508 7.545 7.546 7.547 7.548 7.549 7.550 7.551 7.552 7.553 7.554 7.776 7.777 7.778 7.779 7.780 7.781 7.782 7.783 7.784 7.785

Telescoping series 60

7.319 7.320 7.321 7.322 7.323 7.324 7.325 7.326 7.327 7.328 7.394 7.395 7.396 7.397 7.398 7.399 7.400 7.401 7.402 7.403 7.446 7.447 7.448 7.449 7.450 7.451 7.452 7.453 7.454 7.455 7.490 7.491 7.492 7.493 7.494 7.495 7.496 7.497 7.498 7.499 7.535 7.536 7.537 7.538 7.539 7.540 7.541 7.542 7.543 7.544 7.766 7.767 7.768 7.769 7.770 7.771 7.772 7.773 7.774 7.775

Absolute and conditional convergence 14

7.239 7.240 7.241 7.242 7.243 7.244 7.245 7.246 7.247 7.248 7.329 7.330 7.331 7.332

Error bounds for series 20

7.299 7.300 7.301 7.302 7.303 7.304 7.305 7.306 7.307 7.308 7.383 7.384 7.385 7.386 7.387 7.388 7.389 7.390 7.391 7.392

Comparison and limit comparison tests 60

7.249 7.250 7.251 7.252 7.253 7.254 7.255 7.256 7.257 7.258 7.333 7.334 7.335 7.336 7.337 7.338 7.339 7.340 7.341 7.342 7.407 7.408 7.409 7.410 7.411 7.412 7.413 7.414 7.415 7.416 7.460 7.461 7.462 7.463 7.464 7.465 7.466 7.467 7.468 7.469 7.509 7.510 7.511 7.512 7.513 7.514 7.515 7.516 7.517 7.518 7.736 7.737 7.738 7.739 7.740 7.741 7.742 7.743 7.744 7.745

Power series from the geometric series 60

7.279 7.280 7.281 7.282 7.283 7.284 7.285 7.286 7.287 7.288 7.363 7.364 7.365 7.366 7.367 7.368 7.369 7.370 7.371 7.372 7.427 7.428 7.429 7.430 7.431 7.432 7.433 7.434 7.435 7.436 7.480 7.481 7.482 7.483 7.484 7.485 7.486 7.487 7.488 7.489 7.525 7.526 7.527 7.528 7.529 7.530 7.531 7.532 7.533 7.534 7.746 7.747 7.748 7.749 7.750 7.751 7.752 7.753 7.754 7.755

Taylor series about a point 14

7.309 7.310 7.311 7.312 7.313 7.314 7.315 7.316 7.317 7.318 7.393 7.404 7.405 7.406

Maclaurin series by substitution 21

7.269 7.270 7.271 7.272 7.273 7.274 7.275 7.276 7.277 7.278 7.353 7.354 7.355 7.356 7.357 7.358 7.359 7.360 7.361 7.362 7.456