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Linear approximation practice problems

Estimate values with the tangent line: L(x) = f(a) + f′(a)(x − a). 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Use the linear approximation of \( \displaystyle f(x) = \frac{1}{x} \) at \( \displaystyle x = 2 \) to estimate \( \displaystyle f(\frac{201}{100}) \).
Problem 3.16easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sqrt{x} \) at \( \displaystyle x = 49 \) to estimate \( \displaystyle f(\frac{249}{5}) \).
Problem 3.17easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{1}{100}) \).
Problem 3.18easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{3}{50}) \).
Problem 3.19easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(- \frac{1}{20}) \).
Problem 3.20easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \frac{1}{x} \) at \( \displaystyle x = 2 \) to estimate \( \displaystyle f(\frac{99}{50}) \).
Problem 3.21easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \ln{\left(x \right)} \) at \( \displaystyle x = 1 \) to estimate \( \displaystyle f(\frac{93}{100}) \).
Problem 3.22easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sqrt[3]{x} \) at \( \displaystyle x = 8 \) to estimate \( \displaystyle f(\frac{42}{5}) \).
Problem 3.23easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sqrt{x} \) at \( \displaystyle x = 81 \) to estimate \( \displaystyle f(\frac{402}{5}) \).
Problem 3.24easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(- \frac{7}{100}) \).
Problem 3.25easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(- \frac{3}{50}) \).
Problem 3.26easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sin{\left(x \right)} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{1}{25}) \).
Problem 3.27easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sqrt{x} \) at \( \displaystyle x = 64 \) to estimate \( \displaystyle f(63) \).
Problem 3.28easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sin{\left(x \right)} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{3}{50}) \).
Problem 3.29easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \ln{\left(x \right)} \) at \( \displaystyle x = 1 \) to estimate \( \displaystyle f(\frac{27}{25}) \).
Problem 3.30easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sin{\left(x \right)} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{1}{100}) \).
Problem 3.106easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \ln{\left(x \right)} \) at \( \displaystyle x = 1 \) to estimate \( \displaystyle f(\frac{21}{20}) \).
Problem 3.107easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sqrt{x} \) at \( \displaystyle x = 9 \) to estimate \( \displaystyle f(\frac{48}{5}) \).
Problem 3.108easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \ln{\left(x \right)} \) at \( \displaystyle x = 1 \) to estimate \( \displaystyle f(\frac{99}{100}) \).
Problem 3.109easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sin{\left(x \right)} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{2}{25}) \).
Problem 3.110easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \ln{\left(x \right)} \) at \( \displaystyle x = 1 \) to estimate \( \displaystyle f(\frac{51}{50}) \).
Problem 3.111easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{2}{25}) \).
Problem 3.112easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \frac{1}{x} \) at \( \displaystyle x = 10 \) to estimate \( \displaystyle f(\frac{999}{100}) \).
Problem 3.113easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(- \frac{9}{100}) \).
Problem 3.114easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sqrt{x} \) at \( \displaystyle x = 64 \) to estimate \( \displaystyle f(\frac{321}{5}) \).
Problem 3.115easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \ln{\left(x \right)} \) at \( \displaystyle x = 1 \) to estimate \( \displaystyle f(\frac{19}{20}) \).
Problem 3.116easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \frac{1}{x} \) at \( \displaystyle x = 4 \) to estimate \( \displaystyle f(\frac{403}{100}) \).
Problem 3.117easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \sin{\left(x \right)} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{3}{100}) \).
Problem 3.118easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = e^{x} \) at \( \displaystyle x = 0 \) to estimate \( \displaystyle f(\frac{9}{100}) \).
Problem 3.119easy✓ Every equation proved
Use the linear approximation of \( \displaystyle f(x) = \frac{1}{x} \) at \( \displaystyle x = 4 \) to estimate \( \displaystyle f(\frac{401}{100}) \).
Problem 3.120easy✓ Every equation proved