2 (a) Derive a formula for the Taylor series expansion of f(x) = using a = 0. 2-x Use f(x) = E f") (x - a)" =f(a) +f'(a)(x – a) + f"(a) (x- a)² + 2! (a) (x - a)³ 3! n! n = 0 " (a) 2 (x – a)* 4! " (a) (x – a)" +... п! Write f(x) = 2-x 2(2 – x) to facilitate differentiation. (b) Find the approximate value of f(x) 2 using the Taylor series obtained above when x = 1.10. 2- Employ zero- to fourth-order versions and determine the absolute true relative percent error e, in each case. Round-off each approximation to 5 significant figures.

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Q: (b) At x = 0, the Fourier series of x - 2, -1 <x S 10, converges to: (A) -2 (B) –1 (C () The colut.

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Q: Find the Taylor series generated by f at x= a. f(x) = -, 1 a = 3 X (x- 3)" Ο Α Σ 3" OA. n =0 (x –…

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Q: Determine the Taylor Series Expansion of these Equations f(x) = x* – 2x³ + 4x² – 2x + 10 = 0 where x…

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Q: 1 Let f(r) (a) Find first four terms of the Maclaurin series for f(x). (b) Use your result to find…

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Q: centered at a=Z Find the taylor series for fcx) =

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Q: Find the Taylor series centered at the origin for the function f(x)=xcos(3x)

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Q: (b) The function x* is periodic with period 21 on the interval (-1,1].Find its Fourier series. (c)…

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Q: 12. Find a Taylor series representation for the function f(x) = sin(x) about a = 2 (a) 1 - (x-7² 2!…

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Q: 6. Let g(x) = -1/² for x 0 and g(0) = 0. (a) Show g(n) (0) = 0 for all n = 0, 1, 2, 3,.... (b) Show…

A: We will use formula of taylor series to solve this problem.

Q: (s) If the Taylor series of a function f (x) is 2n(n + 1) n=1 (a) identify Cn- (b) find f(4) (0).

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Q: If f is the Fourier series of [3, -4<x<0 [ 16 – x², 0 ≤ x < 4 g(x): = = I f(x) COS ƒ(z) = ¯ + 2 [()…

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Q: (a) Show that the p.d.f. of Zf is given by g1(r) = e-(+)cosh(vAr), z > 0, where cosh(2) = (e +e) is…

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