(b) Ir(t) x u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of the derivative.

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: (c) f''(x) = cos x, f(0) = 1, f'(0) = 2, f"(0) = 3.

A: Explained below

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A: ∫x2+a2 dx = xx2+a22+a22lnx+x2+a2+C

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A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: b) S X sin xdx 0.

A: Integral by parts:∫uv dx =u∫vdx -∫dudx ∫vdx dxu=xv=sin x∫ vdx =∫sinx dx = -cos x+Cdudx=ddx(x)=1

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A: Indefinite integral

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Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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A: The given function is: f(x)=e-5x

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