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In problems 37-40, find a Power series representation for the given function centered at x = a. 37. f(x) 39. 3 6x+2 f(x) = 2x² x²+1 a = 0 a = 0 38. 40. f(x)= = f(x) = = 3 x+2 a = 5 2 3-2x-x² a = -1 (complete sq.)

In problems 37-40, find a Power series representation for the given function centered at x = a. 37. f(x) 39. 3 6x+2 f(x) = 2x² x²+1 a = 0 a = 0 38. 40. f(x)= = f(x) = = 3 x+2 a = 5 2 3-2x-x² a = -1 (complete sq.)

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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In problems 37 – 40, find a Power series representation for the given function centered at \( x = a \). 37. \( f(x) = \frac{3}{6x+2} \quad a = 0 \) 38. \( f(x) = \frac{3}{x+2} \quad a = 5 \) 39. \( f(x) = \frac{2x^2}{x^2+1} \quad a = 0 \) 40. \( f(x) = \frac{2}{3-2x-x^2} \quad a = -1 \) (complete sq.)
Transcribed Image Text:In problems 37 – 40, find a Power series representation for the given function centered at \( x = a \). 37. \( f(x) = \frac{3}{6x+2} \quad a = 0 \) 38. \( f(x) = \frac{3}{x+2} \quad a = 5 \) 39. \( f(x) = \frac{2x^2}{x^2+1} \quad a = 0 \) 40. \( f(x) = \frac{2}{3-2x-x^2} \quad a = -1 \) (complete sq.)
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