Problem

Use the definition of a Taylor series to find the…

03:11

Problem 7 Medium Difficulty

Use the definition of a Taylor series to find the first four nonzero terms of the series for $ f(x) $ centered at the given value of $ a. $

$$ f(x) = \sqrt [3]{x}, \quad a = 8 $$

Name: use the definition of a taylor series to find the first four nonzero terms of the series for fx ce 3
Uploaded: 2018-04-07
Duration: 3 min 31 s
Channel: Numerade
Description: Use the definition of a Taylor series to find the first four nonzero terms of the series for $ f(x) $ centered at the given value of $ a. $ $$ f(x) = \sqrt [3]{x}, \quad a = 8 $$

Answer

$$2+\frac{1}{12}(x-8)-\frac{1}{3^{2} \cdot 2^{5}}\left(x{-8}\right)^{2}+\frac{10}{3^{3}} \cdot \frac{1}{2^{5} \cdot 3 !}(x-8)^{3}$$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Discussion

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Video Transcript

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Wen Z.