Show that if L{f(t)) = F(s) then L{"f(1)} = F(s-k) where k is a constant. Hence find: (a) L{" sin bt} (b) L(e" cos bt} where a and b are constants in both cases.

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A: We can find the integration as below

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A: We can find the value of f(x) as below.

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A:

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A: a=2 b=-1 c=3

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A:

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A:

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A: we have to find domain

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A: Given a. f(x)=cot4x+cscxb. f(x)=sin2xtanx

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A: Solution of given question is followed by:

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A: see 2nd step.

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A: Given problem:- f''(θ) = sin(θ) + cos(θ) , f(0) =2 , f'(0) =2  To find:- f(θ)

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A: Find the derivative of the following function

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A: The solution is given below

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A:

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A: We have to find the derivative of f(r)

Q: If sinh(æ) = -4 , then coth(x) = (A) (B) =VI7 (C) =VE V15 (D) 4 15 (E) E O (A) O (B) o (c) O (D) O…

A: Solution

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A:

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A:

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A: f''(θ)=sin(θ)+cos(θ)Integrate with respect to θf'(θ)=∫sin(θ)+cos(θ) dθ f'(θ) =-cos(θ)+sin(θ)+C1Again…

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A: