00For |r| < 1, > n(ar)" = ar + 2(ar)² + 3(ar)³ + ... =arUse this to find the power series for f(x) =•.. --x(1 – ar)?(1+x)n=1Select the correct answer below:O 2 n(x)"n=100O 2 n(-x)2"n=1(-x)"nпn=1O > n(-x)"n=1(x)"пn=100O 2(-nx)"n=1

Answered: Image /qna-images/answer/801398b3-352d-4070-9a4f-b69da58924a8.jpg

Answered: 00 ar For Ir| < 1, Σn(ar" = ar + 2(ar)?…

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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3. Given the Maclaurin series I calculated for f(x)= sinx from the video on Maclaurin series, write down a power series for sin(x)
Use the power series 00 E(-1)^x" 1 + x n = 0 to determine a power series, centered at 0, for the function. 1 dx х+ 1 f(x) = In(x + 1) = f(x) = > n = 0 Identify the interval of convergence. (Enter your answer using interval notation.)
(2n)! Find a Maclaurin series for f(x). (Use for 1:3.5. (2n - 3).) --. 2"n!(2n-1) f(x) = 1 + f(x) = x + 16 n = 2
1 g(x) = (7 +x)3 g(x) = 2 5 „n (-1)"(n+1)(n + 2) 2.(7)"+3 n=0 Part 3 Use your answers above to now express the function as a power series (centered at x = 0). x2 h(x) = (7 + x)3 h(x) = n=0
(2n+ 1)x Please explan Determine whether the series sin- converges or diverg es. If it converges, find its sum. thish L and how it nelotes to the n-D0 (4r + 1)x Since sin =1 and sin =-1 and the angle may be incremente by any multiple of 2x, then sin 2 =1 and (4r+3)a sin =-1, (any r). How does this nelate to the answer. Examine the partial sums of the series. The expanded series is sin 3n 5x + sin + sin ,+ sin + sin+ .. ansver Notice that the angles in consecutive even terms (n is even) differ by 2x, and the angles in consecutive odd terms (n is odd) differ by 2x. Since sin 0 = sin (0+2mx), all the even terms are equal to 1, and all the odd terms are equal to -1. Evaluating each term, the series is 1+(-1)+1+(-1)+1+ The partial sums altermate between 1 and 0, tending to (2n + 1)a neither value. Therefore, lim sin- k00 n=0 does not exist and the series diverges. detail. Pelease explain n thanke gou.
Use a power series to represent the following function: f(x)=x^2/2-x

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00 ar For Ir| < 1, Σn(ar" = ar + 2(ar)? + 3(ar) + ... = Use this to find the power series for f(x) = (1 – ar)? (1+x)² * n=1 Select the correct answer below: 00 O 2 n(x)" n=1 00 o 2n(-x)²n n=1 00 (-x)" n=1 00 E n(-x)" n=1 (х)" n=1 O 2-nx)" n=1