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Back to Finding and using Taylor series

Activity 8.5.2

Avg difficulty 2.5

Use known Taylor series and substitution and algebraic techniques to find a Taylor series representation for each of the following functions. In addition, state the interval of xx-values for which you expect each Taylor series to converge.

  1. g(x)=x3sin⁡(x2)g(x) = x^3 \sin(x^2)

  2. h(x)=e−x4h(x) = e^{-x^4}

  3. p(x)=11+5xp(x) = \dfrac{1}{1+5x}

  4. q(x)=x2ln⁡(1+x4)q(x) = x^2\ln(1+x^4)

  5. r(x)=e3x−13xr(x) = \dfrac{e^{3x}-1}{3x}

Boelkins, Active Calculus, §8.5 Finding and using Taylor series, Activity 8.5.2

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Adapted from Active Calculus © 2012–2025 Matthew Boelkins. Licensed under CC BY-SA 4.0. Source: Active Calculus. Imported at revision dc86ba3.