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Taylor and Maclaurin polynomials practice problems

Polynomial approximations built from derivatives at a point. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = \ln{\left(x + 1 \right)} \).

Problem 7.42medium✓ Every equation proved

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = \operatorname{atan}{\left(x \right)} \).

Problem 7.45medium✓ Every equation proved

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = \frac{1}{1 - x} \).

Problem 7.93medium✓ Every equation proved

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = \cos{\left(x \right)} \).

Problem 7.99medium✓ Every equation proved

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = \sin{\left(x \right)} \).

Problem 7.104medium✓ Every equation proved

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = e^{x} \).

Problem 7.105medium✓ Every equation proved

Find the Maclaurin polynomial of degree 3 for \( \displaystyle f(x) = \sqrt{x + 1} \).

Problem 7.31hard✓ Every equation proved

Find the Maclaurin polynomial of degree 4 for \( \displaystyle f(x) = e^{x} \).

Problem 7.32hard✓ Every equation proved

Find the Maclaurin polynomial of degree 4 for \( \displaystyle f(x) = \sin{\left(x \right)} \).

Problem 7.33hard✓ Every equation proved

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = \sqrt{x + 1} \).

Problem 7.34hard✓ Every equation proved

Find the Maclaurin polynomial of degree 3 for \( \displaystyle f(x) = \operatorname{atan}{\left(x \right)} \).

Problem 7.35hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = \sqrt{x + 1} \).

Problem 7.36hard✓ Every equation proved

Find the Maclaurin polynomial of degree 4 for \( \displaystyle f(x) = e^{2 x} \).

Problem 7.37hard✓ Every equation proved

Find the Maclaurin polynomial of degree 3 for \( \displaystyle f(x) = \frac{1}{1 - x} \).

Problem 7.38hard✓ Every equation proved

Find the Maclaurin polynomial of degree 4 for \( \displaystyle f(x) = \cos{\left(x \right)} \).

Problem 7.39hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = \frac{1}{1 - x} \).

Problem 7.40hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = \operatorname{atan}{\left(x \right)} \).

Problem 7.41hard✓ Every equation proved

Find the Maclaurin polynomial of degree 3 for \( \displaystyle f(x) = \sin{\left(x \right)} \).

Problem 7.43hard✓ Every equation proved

Find the Maclaurin polynomial of degree 2 for \( \displaystyle f(x) = e^{2 x} \).

Problem 7.44hard✓ Every equation proved

Find the Maclaurin polynomial of degree 4 for \( \displaystyle f(x) = \ln{\left(x + 1 \right)} \).

Problem 7.91hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = \ln{\left(x + 1 \right)} \).

Problem 7.92hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = \sin{\left(x \right)} \).

Problem 7.94hard✓ Every equation proved

Find the Maclaurin polynomial of degree 4 for \( \displaystyle f(x) = \operatorname{atan}{\left(x \right)} \).

Problem 7.95hard✓ Every equation proved

Find the Maclaurin polynomial of degree 4 for \( \displaystyle f(x) = \sqrt{x + 1} \).

Problem 7.96hard✓ Every equation proved

Find the Maclaurin polynomial of degree 3 for \( \displaystyle f(x) = \ln{\left(x + 1 \right)} \).

Problem 7.97hard✓ Every equation proved

Find the Maclaurin polynomial of degree 3 for \( \displaystyle f(x) = e^{2 x} \).

Problem 7.98hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = \cos{\left(x \right)} \).

Problem 7.100hard✓ Every equation proved

Find the Maclaurin polynomial of degree 3 for \( \displaystyle f(x) = \cos{\left(x \right)} \).

Problem 7.101hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = e^{x} \).

Problem 7.102hard✓ Every equation proved

Find the Maclaurin polynomial of degree 5 for \( \displaystyle f(x) = e^{2 x} \).

Problem 7.103hard✓ Every equation proved