Find the first four nonzero terms of the Taylor series for the functions (1 + x2)-1/3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Find the first four nonzero terms of the Taylor series for the functions (1 + x2)-1/3

Expert Solution
Step 1

Consider the given function.

fx=1+x213

The Taylor function is defined as,

fx=fa+xaf'a+xa2f''a2!+xa2f'''a3!+

The value of a is not given in the question. Let x=0 for the given condition.

now, find the derivative and calculate the values.

f1=12

Step 2

And, the derivative and their values.

f'x=x1+x232f'1=11+132=123

And,

f''x=2x2+11+x252f''1=2+11+152=125

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