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4 n=n? + 2n 1 4. Σ -(x-3)"

4 n=n? + 2n 1 4. Σ -(x-3)"

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 4 please
8.2 EXERCISES In Problems 1-6, determine the convergence set of the given power series. 2™" 1. Σ -(x-1)" n=on + 1 Q to. Al hood of xo to a function has to be the Taylor series of that function. For example, the expar for arctan x given in (9) of Example 2 must be its Taylor expansion. рс With these facts in mind we are ready to turn to the study of the effectiveness of series techniques for solving differential equations. In the next sections, you will find it hel to keep in mind that if fand g are analytic at xo, then so are f+g, cf, fg, and f/g if g(x) = These facts follow from the algebraic properties of power series discussed earlier. 12 3 2. E $ 00 3" n=on!" 4 R 21-22 X² 888 5 T 6 When the expansion point xo is zero, the Taylor series is also known as the Maclaurin series. X & 7 00 3. Σ(x+2)" 3 5. Σ'(x-2)" n=1 n n=0 8 1 ( 9 I 4. ) 6. 00 4 Σ n=1n² + 2n (n+2)! n! $10 ∞o n=0 -(x-3)" -(x + 2)"
Transcribed Image Text:8.2 EXERCISES In Problems 1-6, determine the convergence set of the given power series. 2™" 1. Σ -(x-1)" n=on + 1 Q to. Al hood of xo to a function has to be the Taylor series of that function. For example, the expar for arctan x given in (9) of Example 2 must be its Taylor expansion. рс With these facts in mind we are ready to turn to the study of the effectiveness of series techniques for solving differential equations. In the next sections, you will find it hel to keep in mind that if fand g are analytic at xo, then so are f+g, cf, fg, and f/g if g(x) = These facts follow from the algebraic properties of power series discussed earlier. 12 3 2. E $ 00 3" n=on!" 4 R 21-22 X² 888 5 T 6 When the expansion point xo is zero, the Taylor series is also known as the Maclaurin series. X & 7 00 3. Σ(x+2)" 3 5. Σ'(x-2)" n=1 n n=0 8 1 ( 9 I 4. ) 6. 00 4 Σ n=1n² + 2n (n+2)! n! $10 ∞o n=0 -(x-3)" -(x + 2)"
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