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Find a power series representation for f. (Give your power series representation centered at x = 0.) f(x) = In (1+x) f(x) = 00 Σ n = 0 Graph f and several partial sums sn(x) on the same screen. 2 Z r -1 1 -1 1 -2 -2 1 2 2 2 -2 What happens as n increases? (Enter your answer using interval notation.) As n increases, sn(x) approximates f better on the interval of convergence, which is 2 1 2 2

Find a power series representation for f. (Give your power series representation centered at x = 0.) f(x) = In (1+x) f(x) = 00 Σ n = 0 Graph f and several partial sums sn(x) on the same screen. 2 Z r -1 1 -1 1 -2 -2 1 2 2 2 -2 What happens as n increases? (Enter your answer using interval notation.) As n increases, sn(x) approximates f better on the interval of convergence, which is 2 1 2 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 16E
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Find a power series representation for f. (Give your power series representation centered at x = 0.) f(x) = In(1+x) 00 f(x) = Σ n = 0 Graph f and several partial sums sn(x) on the same screen. 3 -2 -2 -1 -2 -3 -2 - 3 1 2 2 -2 -2 1 -1 What happens as n increases? (Enter your answer using interval notation.) As n increases, s₁(x) approximates f better on the interval of convergence, which is 2 1 -1 -2 -3 2 -1 -2 -3 1 1 2 2
Transcribed Image Text:Find a power series representation for f. (Give your power series representation centered at x = 0.) f(x) = In(1+x) 00 f(x) = Σ n = 0 Graph f and several partial sums sn(x) on the same screen. 3 -2 -2 -1 -2 -3 -2 - 3 1 2 2 -2 -2 1 -1 What happens as n increases? (Enter your answer using interval notation.) As n increases, s₁(x) approximates f better on the interval of convergence, which is 2 1 -1 -2 -3 2 -1 -2 -3 1 1 2 2
Express the function as the sum of a power series by first using partial fractions. 12 f(x) 2x 35 00 f(x) = Σ n = 0 x² Find the interval of convergence. (Enter your answer using interval notation.) (-19,19) * Need Help? Read It Watch It
Transcribed Image Text:Express the function as the sum of a power series by first using partial fractions. 12 f(x) 2x 35 00 f(x) = Σ n = 0 x² Find the interval of convergence. (Enter your answer using interval notation.) (-19,19) * Need Help? Read It Watch It
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