If F (S), G (S) is a Laplace transform of the two functions f (x), g (x), respectively. So probve that F(S) =SG(S). If yo know that: sinu f(x)= cos.x cosu du + sin. %3D np- cos u sinu du du - g(x) = sinx] 2au - cos x

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A: note :Since you have posted question with multiple sub parts, we will provide the solution only to…

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Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

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Q: Let f(z) = cos and g(z) = tan-(10z) Then if h(z) S(z) find: 9(z) h'(1) = N(즉) = |

A: The given functions are  f(x) = cos-1x/5 , g(x) = tan-110x   If, h(x) = f(x)/g(x)  Find h'(x) and…

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Q: ,2 Compute x² cos(x³ + 3) dx

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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)*…

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Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

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Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

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Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

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Q: Find the Fourier coefficients of the function f(x) = sin(10x) cos(x).

A: Given function is Noted that for a function for which fourier series exists, it is of the following…