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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
329-330
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
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) *
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