CALCULUS:GRAPHICAL...,AP ED.-W/ACCESS
5th Edition
ISBN: 9780133314564
Author: Finney
Publisher: SAVVAS L
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Use the power series = (-1)"x" to determine a power series centered at 0 for the function f(x) = -
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(8x + 1)2
8r +1
O Eo(-8)"(n– 1)x"-1
O Eo(-8)"zx"-1
O Eo(8)">x"
O Eo(8)"zx"-1
O Eo(-8)"x"
Use the geometric series to find the series representation for f(x) = 1/(1+x^2) . Use it to prove what is in the picture!
f® (0) xk:
k!
Constructing a power series of the form E
Using f(x) = sin x, construct the power series
Lk=0
k!
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- The function f(z) = 3 z ln(1 + 2x) is represented as a power series Find the following coefficients in the power series centered at zero: help (numbers) help (numbers) ao 8 = -2 a1 = a2= a3 = -2 83 help (numbers) 00 f(z) = Σan 2". n-0 help (numbers)arrow_forwardUse the geometric series to derive a power series for the function f(x) = 1 / (1-x). What is the radius of convergence for this power series?arrow_forwardFind a power series centered at 2 forf (x) 4 x+2 2 Eo (-1)" (5)" n Eo (–1)" ( *²)" 100 x-2 4 100 X-2 п Zn=0 ()" 100 n In=0arrow_forward
- Find a power series representation for x2cos(2x) and then by differentiation, show that the equation below is correct. Please answer and full detail and write it clearly,arrow_forwardFind the power series for the functions below. Write your answers with the sum starting at n=0 a) f(x) = ln (x+1) b) r(x) = x^4/(1+2x)^3 ( 1+2x in the parenthesis raised to the power of 3).arrow_forwardFind the MacLaurin Series for f (x) = cos(2/x) (-1)"(2x)" (2n)! -x+ 등-. 3 = 1 – x + 6 90 .. (-1)"(4x)" (2n)! = 1-2x + 을x2-.. 2 2 4 Zn=0 45 .. (-1)"x2" (2n)! .2 = 1 – * + - X. Zn=0 2 24 720 .. (-1)"x" (2n)! = 2 – x + - 100 3 Zn=0 720 ..arrow_forward
- (b) Now, lets evaluate the same integral using power series. First, find the power series for the function 24 f(z) Then, integrate it from 0 to 2, and call it S. S should be an infinite series. ² +4 What are the first few terms of S? ao = 12 aj = 12 12 a3 12 a4 = (c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of r in terms of an infinite series. Approximate the value of r by the first 5 terms. 1052 315 (d) What is the upper bound for your error of your estimate if you use the first 10 terms? (Use the alternating series estimation.) 4 23arrow_forwardwith process/explanationarrow_forwardUse the power series X f(x) = (1-x)² Select one: a. c. x e. Ση·(-1)*·(x)" n = 1 x 1 1-X Ση·(x)+1 n = 1 En.(x)" n = 1 = d. Σn (-1)" (x)” +¹ n = 1 Σn. (x)n-1 n = 1 x Σx", x<1 to determine a power series for the function n=0arrow_forward
- I need help on this. Thank youarrow_forward= cosx to find first four terms Use the Maclaurin Series for w(x) = e*and q(x) for nonzero f (x) = w(x) · q(x) Write down the first four terms in the binomial series for (1 + 5x)-4arrow_forwardVerify that Jp+1(x) + 2J½ (x) – Jp-1(x) = 0 Tip: Compare the series of Jp+1(x) – Jp-1(x) and – 2J½(x) = 0arrow_forward
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