f(t) = e¯3t cos ( at + cos ( 2at + 3 2

Q: T/4 ttant dt 2+ cos t -7/4

A:

Q: Find f(x).

A: Given,

Q: Find f. f(0) = = f"(0) = sin(0) + cos(8), f(0) = 3, f'(0) = 2

A: f"θ=sinθ+cosθ Integrating both sides  ∫f" θdθ=∫sinθdθ+∫cosθdθ f'θ=-cosθ+sinθ+C..... (i)  Put θ=0…

Q: Q1/: a: Using the relation showthat Jv2 (x) =, cos x

A: See the attachment

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(71/2) = 0 %3D %3D

A:

Q: O t-sin(t)

A: the answer is t-sin(t)  provided the solution below with steps in step2

Q: Evaluate L{t°e! e3(1 – t) 3e-t sin (4t - 2) 2) + t2 $ (3t)} cos

A: Explanation of the answer is as follows

Q: Evaluate cos¹ (5x) sin(5x)dx + C

A:

Q: Find f if f"(x) = 2+ cos(x), f(0) = 2, f(t/2) = -2.

A:

Q: 1+ csc x cos x + cotx

A: Given query is to simplify the expression.

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

A:

Q: | 1' cos(T +1) dr. COS

A: using the integration by parts

Q: Find L {f(t)} if f(t) = cos 5t + sin 2t

A:

Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: Let Find f(x) = y = f(x) = 5x + 18 cos x. d f(x) =

A: Given query is to find the derivative at indicated point.

Q: ution t= tan 2 tan). os(x)

A: We have to choose the correct answer from the given option

Q: A power signal which is periodic with period 2n and is characterized by the form f(x) Expand f(x) in…

A: Given, fx=sinhxcosx, -π≤x≤π Since, f is periodic of period 2π then, fx+2π=fx Then,…

Q: Find F(s). F(s) = L(1 et + 3e-4t) cos(2t)} -

A:

Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

A:

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

A:

Q: // (cos (a? + y³)dA where D: {(x, y) | 4 < x² + y² < 49} Find

A:

Q: Find the analystic function f(z)u+iv if u=a(1+cos0)

A:

Q: Determine f,(x); f(x) = cos(2x³ +n²)

A:

Q: : (a) Evaluate S cosx sinx V1 – sin+x_dx. (b) Evaluate S V1 – x² dx.

A:

Q: Find f. f"(8) = sin(e) + cos(e), f(0) = 5, f'(0) = 4 f(e) = 5t – sin (t) – cos(t) + 6

A: Here we have f''θ=sinθ+cosθ, f(0)=5, f'(0) = 4 fθ=?

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…