Q 3. Find the Taylor series of f at the point c for : (a) f(x) = e", c= 2 (c) f(x) = sin x, c= T (b) f(x) = }, c = 1 (d) f(x) = cos x, c= 5

Q: find 5 th terms of the function{ sin(2x) }using Taylor series at a= pi/6

A: We will find out the required term.

Q: The first derivative of the power series D (-1)" (2x)" is n! f(x) = n=0

A: Given : fx=∑n=0∞-1nn!2xn As    e-ax=∑n=0∞-1nn!axn∴e-2x=∑n=0∞-1nn!2xn Therefore, fx=e-2x   .....1

Q: 5. (a) Find the Taylor polynomial T2(x) of f(x) = V (= x'/3) centered at a = 1. %3D (b) Let T2(x) be…

A: f(x)=x3To Find:a) Taylor polynomial of f(x) centered at a=1b) Use Lagrange's error bound to justify…

Q: Given f(1) = zsin(z) for -≤x≤ and answer the following questions. 1. Find the Fourier series of f(z)…

A:

Q: Consider the function f(x) = (8)3. We want to find the Taylor series of f(x) at x=7 and at x = -5.…

A: ### (a) Finding the nth Derivative of  f(x)The function is f(x)=(8−x)32​. To find the nth…

Q: (-1)" The first derivative of the power series f(x) =) - (6x)" is O -6 f(x) O f() O-f(x) %3D 0 6…

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Q: Q1: Expand in a sine-Fourier series: f(x)=x,0 < x < 1.

A:

Q: O Let f (x) be a function which is represented by the power series f(x) =E(-1)"-1)". n3 What is the…

A: Power series of fx about x = a isfx = ∑n=0∞fnan!x-an              —⊛

Q: f(x) = cosh(x); -T <x< T etch the function. Determine whether it is even or odd. Expand it in an…

A: Expand the given function in an appropriate Fourier series.

Q: a. b. Taylor polynomial P₂(x) for the function f(x)= e cos x about x = 0. Use P₂(0.5) to approximate…

A:

Q: Find the solution to the ODE using power series solutions   (x-1)y''+3y=0

A:

Q: q18. Let f be a function with a period 2π such that f(x) = −1 if 0 < x < π, f(x) = 1 if π < x < 2π,…

A:

Q: Let f(x): Compute f(x) = f'(x) f"(x) f""(x) = f(iv)(x) = f(v)(x): = = = = 4 + 4x X We see that the…

A:

Q: 18 Given the power series F(x)= 2 (-1)" (x-3)" n= 0 2" Find the derivative for the power series…

A: Answer to the question as follows:

Q: Let f(x) be the function which is represented by the power series : f(x)= E (-1)"(x-2)" Zn=1

A: Given f(x) function represented by the power series We need to find the 5th derivative of f(x) at…

Q: (7) a) Differentiate term by term to find f'(x) for the series f(x)=>; and express the n! n=0…

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Q: f(x) = |sin(x)| Find the Fourier Periodic in the range -n<x<N series expansion of the function.

A:

Q: if the Legendre polynomials P.(x) = -1 then: Find 1) ,x* P,(2) dx 2)P'(-1) A) L P.) dx = and P,(1) -…

A:

Q: Find the degree 3 Taylor polynomial approximation to the function f(x) = 8 ln(sec(x)) about the…

A: Given, f(x)=8(ln(sec(x))) Find Taylor polynomial of degree 3 about the point a=0 we know that

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A:

Q: (8) a) Using the Maclaurin series for f(x )= cos x find the first four nonzero terms of cos( x' ).…

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Q: The function f(x) = Cosh(x) can be expressed by Taylor series as follow: Cosh (xi) 2!…

A:

Q: 5. (a)Find the Fourier sine series for f(x) = x³ – n²x on the interval [-7, T]. (b) By plugging in a…

A: For (a), We need to find the Fourier sine series for the function, f(x) = x3 - π2x on the interval…

Q: find Fourier series on [0,2n] オーズ 0<x<T (12) f(x) = Tくx<2元

A:

Q: (-1)" (13z)" is 00 The first derivative of the power series f(x) = n! O -13 f(x) O f(x) O - f(r) O…

A: We need to evaluate the first derivative of the following power series : fx = ∑n=0∞-1nn!13xn

Q: 6. Find the Taylor polynomial T,(x) for the function f(x)= cosx at a="/ it to estimate cos(29780)

A:

Q: (8) (a) Compute the Fourier sine series for the function f such that f(x) = x² on the interval [0,…

A: Fourier series is the expansion of a periodic function as the sum of linear combinations of sine and…