L-¹{F(s)} = ? O Let F(s) = ( O 1 1 s²+64 S5 + f(t) = (sin(8(t-7)) 8 f(t) = (sin(t-8) + O f(t) = (cos(8 (t-8))+ (t−7)4) u(t-7) O (t-7)4 f(t)= (sin(8(t-7))+ 4! -7 S -) e¯7s then (t-7)4 + -) u(t-7) 4! (t-8)4 4! O None of the others -) u(t-7) -)u(t-8)

Q: Evaluate / 4 x cos(x)dx Ox sin(x) – 4 cos(x) + c 04 sin(x) + 4 x cos(x) + c 04 (x sin(x) + cos(x)) +…

A:

Q: Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) +…

A: Answer is given.

Q: |(estn(5c))(cos(5c))(dc)

A: Given: ∫esin5ccos5cdc Now by using the substitution u=5x du=5…

Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

A:

Q: Suppose S (x) =sin(3x – 2). Evaluate: /f(x) dr A - 3cos(3x – 2) + C (A) (B ® --cos(3r – 2) + C ©…

A: Given, f(x) = sin3x-2To evaluate:∫f(x) dx This can be done as follows:

Q: L{t sin t cos t} = 2s (A) (s²+4)2 -2s (B) (s²+4)² (C) 14) (s²+4)² -8 (s²+4)2 (E) (s²+4)²

A:

Q: O t-sin(t)

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

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: Find f), (b) f(r) tan(2r)

A: To find f’(x).

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

A:

Q: Use the formula £{t^f(t)} (s) = (-1)^(((s)) to help determine the following the expressions. (a) L(t…

A: Solution:-

Q: Evaluate L{2t e2t sin (3t) – e3(1-1) + 3et sin (4t – 5)}

A:

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: d (c) (cos(2²) + In(3 – 2æ)) dx

A:

Q: MacB = (x),ƒ o (1)fp хр = (x),f o %3D (x)fp = (x),f O %3D xp = (x),f o = sin x, which of the…

A: To find the correct option.

Q: Find the value of f(0) when 3 sin(2t), f( f'(t) 1. f(0) 2. f (0) 3. f (0) 4. f(0) 5. f(0) = = = = =…

A:

Q: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

Q: Evaluate L{t cosh 4t. 1 1 + (s – 1)’' (s+1)* А. В. (s-1)* (s+1)* 1 1 С. (s –4)° (s+4)' 3. D. (s-4)*…

A:

Q: v (m/sec) 0 A 2 3 4 6 →t (sec) -2/ f(x)dx

A: Solution:Given       for x=5  y=0and x=3     y=2f(x)=5-xTo find∫35f(x)dx=?

Q: f (t) =-e" sin (21 +7)

A:

Q: 1. (D² - 4D+5) (e² sin x)

A:

Q: COs ax dx. x² + b² (q)

A: Cauchy residue theorem: If f is holomorphic function defined on simply connected open set with…

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…

Q: 4 Let f(x) = 6x°va + || f'(x) =

A:

Q: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

A:

Q: (d) v1+ tan x =1+;x

A: To prove that the following approximation holds, 1+tanx≅1+12x

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 8 8 + 4 sin(3x)cos(3x), sin(2x) +…

A: