In each of Problems 1 through 10, find the Fourier cosine and sine integral representations of the func- tion. Determine what each integral representation converges to. x* for 0 10

Q: Compute the following. d [7x11+3x7-23x +14x12/7+5x-3+43] dx

A: we know that d(xn)dx=nxn-1

Q: Evaluate the integral (4x -7/13 – 5x13)dx. „7/13 (4x -7/13 - 5x13)dx help (formulas) -

A: We first distribute the integration

Q: Problem 5. Define () to be the value n(n – 1)/2. Calculate the following: Part A. Calculate (;), C),…

A: We are given the formula for calculating the combinations as, Part A : Part B : This gives,

Q: Show that Loo (1 COS X (1+x²)² dx кіо π e

A:

Q: a. Sketch the graph of the given function for three periods. b. Find the Fourier series for the…

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Q: D. State the amplitude of the given function f(x) = 5 sin [ 4 (x – 30°)] - 2

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Q: 1/4 1 √1/12 √x(4x + 1)' dx

A:

Q: 7. Prove that d dx [cos ¹ x] = = 1 √1-x² x2

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Q: It can be shown by induction that the nth derivative of the sine function is given by the formula d"…

A: Givendndxn(sin x)=-1n-12cos xn odd(-1)n2sin xn evenTo findwhether the given formula is correctTo…

Q: Find ſ x²e-0.5x dx

A:

Q: Compute the following.   d/dx(3x+5)2 x=1

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Q: 2. Find each of the following transforms: (a) L[x² sin ax];

A:

Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: 1.A.5. Show that in the range - <x<* 00 sinh kr Σ (-1)n-1 (24²) sin nx n=1 sinh kx = --²/4 where k…

A: (.) Given function is,   h(.)  Fourier series of a function  in the interval  i.e.  is given by,…