4. f(t)5. f(t)==ΜεΣn = 08Σn=0(-1)^4ntn5n+14ntn5n+1 Find a power series representation for thefunction1. f(t)2. f(t)3. f(t)===f(t)i M8 IM8 M8n=0n=0n=0=15 + 16t²(−1)n 4²nf 2n5n+1(−1)n 42n + 2n5n42n+2n5n+1

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Answered: Find a power series representation for…

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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Find a power series representation for the function on (-1, 1). 1. f(x) 2. f(x) 3. f(x) 4. f(x) = 6. f(x) = = = f(x) 22 tan = α Σ n = 0 Σ n=0 α n=0 5. f(x) = Σ n=0 Σ n = 0 α Σ n=0 = 1 n+1 (-1)" 2η + 1 xn+3 1 2n + 1 −1)n n+1 -1(2) x²n+3 x2n+3 xn+3 (-1)" (2n + 1)! x²n+3 (−1)n xn+3 (n + 1)!
Q2: Find the Fourier series of the function. π + if- πt<0 2 r(t) = r(t + 2n) = r(t) %3D if 0
0 A projectile fired from the ground follows the trajectory given by the following equation, where is the initial speed, is the angle of projection, g is the acceleration due to gravity, and k is the drag factor caused by air resistance. y =tan(0) + = (tan y = tan (0)x Using the power series representation In(1 + x) = x - x² 2 y =tan(0) + y = (tan(0))x g kvo cos(8) 00 g g kvo cos(8) ) x + 2/2 In (1 k² 9x² 2v² cos²(0) √))x + ²/² ( ²₁ 5-) g Σ n = 1 n = 2 kx Vo cos(8) + x3 3 4 + kgx³ k²gx4 3v³ cos ³ (0) 4v4 cos4(0) -1 < x < 1, verify that the trajectory can be rewritten as the following.
14
i need aacurate solution of both parts if u know both parts then u try otherwise not
2. Find the Fourier series for the function f(x) = |x|, -T < x < T; f(x+ 27) = f(x). Use this series to find the sum for the infinite series E . n=1 n2:
(a) Find a power series representation for the function. 2 f (x) = 11+ x n+1 2 E(-1)" (#) 11 n=0 1 2(-1)"+1, n=0 1 iE(-1)" 2"+1" n=0 1 (–1)" TT 11n+1 n=0 2(-1)" 11" n=0 (b) Determine the interval of convergence. ? ?
(a) Find a power series representation for the function. (Give your power series representation centered at x = 0.) (2) = 22+1 2.12 + 1 E(-1)" 2"+1,n+1 2(-1)" 1an+1 E(-1)" E(-1)" 2".2" E(-1)" 2".-2n+1
Show COMPLETE solutions. Box the FINAL answer.
4x - 10 Let f(x)=1-(2x-5)4¹ a. Find the Taylor series representation for f about x = 2.5 that is valid for all x € (2,3). Hint: Use the equation t", where t € (-1,1), to find the Taylor series representation for x=0 1 about x = 2.5. Then, use this series to find the desired series representation for f. 1-(2x-5)* b. Use the result in item 2(a) to find the 5th degree Taylor polynomial of f about 2.5. c. Use the result in item 2(b) to approximate f(2.55). Express your answer in decimal form. +00
Find the Fourier series representation of the periodic function below if a = 18, c = 4, k = 9, and L = 10. Then, evaluate the first few terms of the series up to n = 5 if x = 1.19.

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Find a power series representation for the function 1. f(t) 2. f(t) 3. f(t) = = = f(t) M8 M8 M8 Σ n = 0 n = 0 n = 0 = 1 5 + 16t² (−1)n 4²nf 2n 5n+1 (−1)n 42nf 2n 57 42n+2n 5n+1