Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Taylor series centered at 0 for the function given below. Give the interval of convergence for the new series. Use the Taylor serie x²x3 for 1sxs1. 16 √1+x=1+28 + √1+x² The first term is The second term is The third term is The fourth term is The interval of convergence is (Type a compound inequality. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Taylor series centered at 0 for the function given below. Give the interval of convergence for the new series. Use the Taylor series
x² x3
8 16
√1+x=1+
√√1+x²
X
2
The first term is
The second term is
The third term is
The fourth term is
+
...for 1 ≤x≤ 1.
***
The interval of convergence is
(Type a compound inequality. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
Transcribed Image Text:Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Taylor series centered at 0 for the function given below. Give the interval of convergence for the new series. Use the Taylor series x² x3 8 16 √1+x=1+ √√1+x² X 2 The first term is The second term is The third term is The fourth term is + ...for 1 ≤x≤ 1. *** The interval of convergence is (Type a compound inequality. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
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