Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

For number 7, the summation notation provided in the answer key, how do we account for the x in the beginning of the polynomial? When typing in 0, I got for the first term is x-3, not x. 

c) E In +3 di) -1)" (x+2)' 10" n=0 n=1 n2" For what values of x does the series converge? What is its sum? What series do you get if you differentiate the series term by term? For what values of x does Questions the new series converge? What is its sum? 2 -가*-3) +(x-3)' +. (x-3) +.. .. If you integrate the series in question 4 term by term, what new series do you get? For what values of x does the new series converge? Find C when x =3. 7. ond 3 for f(x)=x+4 generated =yx+4 generated 6.
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Transcribed Image Text:c) E In +3 di) -1)" (x+2)' 10" n=0 n=1 n2" For what values of x does the series converge? What is its sum? What series do you get if you differentiate the series term by term? For what values of x does Questions the new series converge? What is its sum? 2 -가*-3) +(x-3)' +. (x-3) +.. .. If you integrate the series in question 4 term by term, what new series do you get? For what values of x does the new series converge? Find C when x =3. 7. ond 3 for f(x)=x+4 generated =yx+4 generated 6.
su 7. If you integrate the series in question 4 term by term, what new series do you get? For what values of x does the new series converge? Find C when x =3. If f(x) = 1 – (x – 3)+ (x 3 + ( )"x_ 3)* +... = then f(x) dx = x - 3 + +(-4)" “„ 3 At x I the series E diverges: at x = 5 the series -1)" 2 n+ 1 converges. Theretore the interval of convergence is I <x<5 and the sum is 2 In x 1+(3 In 4), since dx = 2 In x1 C, where C 3 SInce In 4 when x= 3. 8. Find the Taylor polynomials of orders 0,1, 2, and 3 for f(x)= Vx+4 generated by f at x 0. 4)/2. f'(x)- ()s f(x)- (x x4)4tN *-() x + 4)2 fi0)- (4)2 2 1/2 1. 5:55 PM a 41°F Clear 昂 12/12/2021
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Transcribed Image Text:su 7. If you integrate the series in question 4 term by term, what new series do you get? For what values of x does the new series converge? Find C when x =3. If f(x) = 1 – (x – 3)+ (x 3 + ( )"x_ 3)* +... = then f(x) dx = x - 3 + +(-4)" “„ 3 At x I the series E diverges: at x = 5 the series -1)" 2 n+ 1 converges. Theretore the interval of convergence is I <x<5 and the sum is 2 In x 1+(3 In 4), since dx = 2 In x1 C, where C 3 SInce In 4 when x= 3. 8. Find the Taylor polynomials of orders 0,1, 2, and 3 for f(x)= Vx+4 generated by f at x 0. 4)/2. f'(x)- ()s f(x)- (x x4)4tN *-() x + 4)2 fi0)- (4)2 2 1/2 1. 5:55 PM a 41°F Clear 昂 12/12/2021
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