1. f(x)=4,0< x<3

Q: Q1: Find the Fourier half range sine series and Fourier half range cosine series of the function…

A: From the graph, the function fx=2x      0≤x≤12         1≤x≤2. Fourier half range sine series:…

Q: Q. 7. Find the Fourier sine series of the function: f(x) = 3x-7, for 0<x<r.

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Q: Q4: (1) Find the Fourier Sine and Cosine series of a function which has constant value at some…

A: Part(a): Consider the function, fx=1,0&lt;x&lt;π20,π2&lt;x&lt;π Expanding the function fx first by…

Q: Approximate cos(x) for /x/< T/4 using Taylor Series (polynomial) with a true error of no greater…

A: Please check step 2 for the solution.!

Q: Queston S Alx) = Xsinx flx)sin x of the following which the Mc-laurin- 78 of the hunction? series…

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0…

Q: -f(x) = x cos x, -π < x < π Find the Fourier series for the following functions:

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Q: x2n+1 Given the Maclaurin series for sin x is sin x = E=0(-1)". find the Maclaurin %3D (2n+1)!'…

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Q: ( 2,-3 < x < 0 Obtain the Fourier series for the function f whose definition in one period is f(x)…

A: Given function is  fx=2,         -3&lt;x&lt;0-2,         0&lt;x&lt;3

Q: Fourier series? f(x)=x² 2 xe logt)

A: Given function is fx=x2, x∈0,π. We have to find the Fourier series of the function fx. The Fourier…

Q: Q # 02: Obtain Fourier sine series and Fourier cosine series for f(x) = x3 in the interval [0, t].

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Q: Q1. Find (i) the Fourier cosine series and (ii) the Fourier sine series of the function f(x) = x, 0…

A: To find the Fourier cosine series, assume the function as even so that the graph of the function…

Q: derivatives, find the Taylor series d fiel=sin X 2) By computing at X=0.

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Q: following periodic function, find its Fourier sine and cosine series. f(1) = { , 0, =\cost, - n <t<…

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Q: B12. (a) Find the Fourier sine series of f(t) = t for 0 <tST. %3D

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Q: for 0< x<1 for i< x<2 Obtain Fourier series for the function f(x) = T(2-x)

A: Fourier series

Q: 0 if 0<x < 1 1. Evaluate the Fourier Sine Series for f (x) = {1 if 1<x < 2 . 0 if 2< x < 4

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Q: 0. || Use power series methods to solve y" + 4xy = 0 at the point xo

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Q: Q5 a) b) (x > 0,k > 0) Find the Fourier cosine integral of f(x) = e-kx Find the Fourier series of…

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Q: ex-(1+x) Evaluate by use Taylor Series lim,0 x2

A: limx→0ex-(1+x)x2

Q: (-1)" 2n+1 Use the power series sin x=E; to approximate (by using four terms) the value of (2n+1)!"…

A: Let's replace x by x2 to obtain: Let's now expand up to four terms to get:

Q: 2. Given: -2,0 <x < 2 0,2 <x < 4 4x, 4 < x < 6 f(x) Calculate the FOURIER SINE SERIES of the given…

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Q: Q #02: Obtain Fourier sine series and Fourier cosine series for f(x) = x3 in the interval (0, z).

A: Consider the given function. fx=x3 The given interval is 0,π. the Fourier sine series of an odd…

Q: Q:) Solve only one from the following. A) Find the half- range cosine series for f(x) = 2x-1,0 <x <…

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Q: O1-A) Determine the half range Fourier Cosine Series for the function ft) = sin t Ostz

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Q: 3+ cos (8x) Perform a test to determine if x converges. 1/8 2 dx x/8 (Type an exact answer, using n…

A:

Q: Q1: Find the Fourier half range sine series and Fourier half range cosine series of the function…

A: Fourier half range cosine series : yx=ao2+∑n=1∞ancosnπ2x

Q: Find the Fourier series for -π<x<0, f(x) = {C 0 <x<n .

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Q: Q.3) Find Fourier cosine series and sine series of the function (0 < x < n/2) f(x) = 7/2 (7/2 < x <…

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Q: x', x* (b) Economize the power series: sin x x- +. 120 5040

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Q: (12x 0 <x < Find the Fourier series of f (x) = on interval –n<x<n. -2 i-n <x < 0

A: Fourier series

Q: g) Find the Fourier sine series of the function f(x)=-100¹0(-<x<n); f(x)= 100¹0 (0<x<n)

A: We have to find the Fourier sine series of the function  f(x)=-10010if -π&lt;x&lt;010010if…

Q: (a) What is the maximum error possible in using the approximation below when -0.2 'ו x| | x| <…

A: In the question we need to put correct values.

Q: Find the Fourier series for the periodic function defined by f(x) = e*, –n < x < n. Hint: Recall…

A: Part (b): To graph the Fourier series of ex in the interval -5π,5π.   We first write the series…

Q: 5. Find the sine series of 0 < x < T/2 Sx, f(x) T – x, T/2 <x<

A: Fourier series

Q: 1-cosx The value of limx→ by using series is 0 sinx True False

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Q: 8+ cos (3x) Perform a test to determine if| dx converges. 13 1/3 00 9 dx 3 1/3 (Type an exact…

A: Answer

Q: x, 0 < x < 1 1. (a) Find the sine series for the function f(x) 2 x, 1 < x < 2 (b) Sketch the graph…

A: Extended f to an odd function to get sine series

Q: Use power series solution to solve the equation. Show a detailed solution (e^-3x) cos(2x) , up to x^

A: The expansion for ex=1+x+x22!+x33!+...... The expansion for cosx=1-x22!+x44!-x66!+....

Q: 2. Find the sine series of Sx, 0 <x < T/2 f(x) п - х, T/2 < x < T

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Q: How do I solve this first order equation using power series? (1-x)y' = y I'm having particular…

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Q: e x - e-x Q2/ A) Find Maclaurin Series for the function sinh x 2 sin x B) Evaluate the integral JJpR…

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Q: 0<x< n n < x< 2n f(x) = lcos x find its Fourier a. Cosine Series b. Sine Series

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Q: 1 |[kcosnt -kcosnt 5. For a certain periodic function f(t) the Fourier coefficient b, - b, when…

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Q: e x - e-x Find Maclaurin Series for the function sinh x 2

A: Maclaurin Series : f(x) = ∑n=0∞f(n)(0)n!xn = f(0) + f'(0) x + f''(0)2!x2 + f'''(0)3!x3 + ⋯   We know…

Q: Q.2: Find the trigonometric Fourier series of the periodic function f(t), and show if it is odd or…

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Q: ex - e-x Q2/ A) Find Maclaurin Series for the function sinh x

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Q: Q1: Find the Fourier half range sine series and Fourier half range cosine series of the function…

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Q: 0.3 11. Use appropriate series to estimate SIn |In(1 + x') dx to 6 decimal place accuracy

A: The estimated value of the given integral upto 6 decimal place accuracy is 0.002009