Use the Laplace transform to find the solution of y"+8 y'+Ay=e¯'sint for y'(0)=y(0)=1 & A=25. Then, determine the largest value of A so that y(t) is a decaying sinusoidal function, ie. y exhibits oscillation but its amplitude approaches zero as t - 00.

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

A: Given: hx=∫0x3cosπt2dt.

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Q: JO (5) Find the derivatives (a) d # t ( * cos(2³) dz + 35e) 4

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: e" sin°(2x) (d) y = In 2x2 + 1

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Q: Find f. f"(0) = sin(0) + cos(0), f(0) = 3, f'(0) = 4 f(0) =

A: Objective is to find f.

Q: Let y -2 = S sin³ (t) dt. Use the Fundamental Theorem of Calculus to find y'. ex

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Q: Use implicit differentiation to find y' for 4x³y² + ln(xy³) Answer exactly. y' (1, 1) = 4 and then…

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Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

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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

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A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

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Q: let y=[cos(2x-π)]3 Find y' at x=(π/6)

A: Compute the derivative as follows.

Q: Find f. f '(x) = cos(x), f(0) = 6, f '(0) = 3, f "(0) = 5

A: Differential equation: f'''(x)=cosx f(0)=6, f'(0)=3 f''(0)=5

Q: Find f. f(0) = f"(0) = sin(0) + cos(8), cos(8), f(0) = 1, f '(0) = 3

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Q: If g(x) = | cos' t dt , then determine g'(x). %3D

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Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: f(z) = cos(4r +5) %3D

A: we have to derivative  we know that  d(cos (ax+b) ) = -sin (ax+b) a                        = - a sin…

Q: Find T, N and B for the curve 7(t) (2 cos(2t), 2 sin(2t), 5t) at the point t = 0 Give your answers…

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Q: find the function of the form y = a sin [b(x-c)] + d with given period, phase shift and range 6, 8,…

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