3. Let: f(x) = In (1+x) a) Use four-digit rounding arithmetic to evaluate f(x) when x = 0.25. b) Replace the logarithmic function with its three nonzero terms of Maclaurin polynomial (show the process in obtaining the Maclaurin series expansion), and use three-digit rounding arithmetic to evaluate f(x) when x = 0.25. c) Compute for the relative error for part (a) and (b).

Q: Expand f(x)=x2−x +2 as a series of Legendre polynomials

A: We expand f(x)=x2−x +2 as a series of Legendre polynomials

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Q: Q2: Find the Fourier series corresponding to the function -k -n<x<0 S(x)3D k 0<x<T

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A:

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A: Let us consider the function f(x) on the interval [-L,L] is obtained as…

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A: Sol:- First check given function is even or odd. fx=xxf-x=-x-x=-xx=-fxHence , given function is…

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A: NOTE: Since we can solve at most three subparts in a question, we have solved the first three…

Q: a. Find Taylor Expansion of the following Functions about xo =0 b. Find Taylor Expansion of the…

A: Sol:- Taylor expansion about x0 = 0 Taylor series of function fx at a is defined…

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Q: 3. Expand the function f(x)=x (4-x²) in the interval -2 ≤x≤2 and period f(x+4)= f(x) to the Fouriér…

A: Solution :-

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A: Given a periodic function xk with period N, the Fourier series is expressed as xk=∑n=0N-1cne2πiknN…

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Q: Write the first three terms of the Taylor series for f(x) =Vx at a = 1. Show your reasoning

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Q: -π<x 0. 0<x<π. 2 f(x) = {?

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Q: Find the Fourier series expansion for the function s(x)=\+(10-x) for (-75xSa)

A: By using the formulas of Fourier series we solve the given problem as follows :

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Q: f(x) = { - O, if, in general, (Draw the graph of f(x))

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Q: A. Find the Fourier series expansion for: f(x) = x +- -n SxS T 4

A: We will expand as shown below

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Q: 2. Let f(x) = 1 3+x Find a Taylor series for f(x) a) by manipulating a know series b) Computing the…

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A: The Taylor series of a function is an infinite sum of terms that are expressed in terms of the…

Q: numerically greatest

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Q: Show that (an) is increasing

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