The signal x() exp(-at)u(t) is passed as the input to a system with impulse response h(t)=sin(2t)/(mt). (a) Find the Fourier transform Y() of the output. (b) For what value of a does the energy in the output signal equal one-half the input signal energy?

Q: Suppose h(x) = cos(tť² )dt Calculate h' (x).

A: Given: hx=∫0x3cosπt2dt.

Q: Part 1: A. Differentiate the following functions with respect to x y = xe ²x (ii) y = 2x³ cos x…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: T (8) If g(x) = sin(x) *cos(x) find g'(-).

A:

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: Suppose that f has an inverse, ƒ(2) = 5, and f'(2) = What is (f~')'(5)? %3D

A: (a) Given that f has an inverse, f(2)=5, and f'(2)=-34 As  f(2)=5 so, f-1(5)=2

Q: Prove that S tan ar tan¹ Br x2 da = 1 log 2 (a + 3)α+³7 Qa38 , a>0, B

A: Note: In the given identity, it should be instead of .We need to prove that , where .Let .

Q: Find f. f(x) = f"(x) = cos(x), f(0) = 9, f'(0): = = 8, f "(0) = 6

A: Given,  f'''(x)=cosx, f(0)=9, f'(0)=8, f''(0)=6

Q: H (x) = VI-Soe? 2. %3D (f09) (><)= H (sc) %3D %3D 9(36) =

A: Given fgx=1-5x2

Q: Determine the phase shift (horizontal shift) of the graph of f (x) = sin(3x + 1) + 2 O O O T ရှိရာ…

A:

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

A:

Q: Chapter 4] If f(x) = dt, where g(x) = 1," (÷) V1+t3 [1 + sin(t²)] dt, find f'

A:

Q: Consider the following. F(x) = dt (a) Integrate to find F as a function of x. F(x) = (b) Demonstrate…

A: Second fundamental theorem : Suppose f is continuous function in an open interval I .Let a∈I and a…

Q: Find f. f(0) = f "(0) = sin(0) + cos(0), f(0) = 1, f(0) = 1, f'(0) = 3

A: Given that the expression

Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: 1. Let A(x) = | e -tdt. (a) Sketch a graph of e-t and use your graph to illustrate what A(x)…

A: Given:Here A(x)=∫1xe-tdtTo find:a)sketch the graph of e-tb)find the value of A(2)c)find…

Q: IfI(u) = [log, (1-2u cos x+ u' )dx, then prove that, I(u)+I(-u)-DI(u²).

A:

Q: where did T/4 come from? I don't understand how we use it to find the phase shift.

A: In the given context, the function being referred to is likely a periodic function that represents…

Q: 2. The population of a certain species of bird in a local sanctuary, P(t), t years after 2020 is…

A:

Q: Let g(x) = [" sin(t²) dt- Calculate g' (3).

A: