Let h(t) = (0 sin(t) Find L {h(t)}. S 0π/2 e-лs/2

Q: Let P(x) dt. Evaluate 2 | P(x)dx. sin

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Q: Let ƒ (t) = e5t sin 7t. Part (a) Find L{f (t)}. Part (b) Find L{f' (t)}.

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Q: (a) Suppose the number of mosquitos in a room can be modeled over time by m(t) = 14 sin(t/12) + 92.…

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Q: 2 1 + x - 1 then find dy when – 1<x <1. If y = tan dx

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Q: g(t) = (t – cos t) sin t. Find g'(t). s

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Q: V3 sin- (x) dx V1 – x² 0.

A: Here we have to find the given definite integral value.

Q: fx = a(0-sin0) and y = a(1- cos 0), find d and d²y/dx².

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Q: 4x Let F be the function defined by F(x) = cos(t?) dt. Find an expression for 3. F'(x).

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Q: (x* +y' )dx+(2xy+ cos y)dy

A: Follow the procedure given below.

Q: 6. Let sin x g(x) = [ Find g (7) 3 3 + -dt

A: Given; g(x)= integraion of sqrt[3/(1/4 +t2)], limit from 1 to sinx.

Q: Q3 Find dy/dx on the graph y3 sec /x2 + y2 = cos2x at point (1, 2).

A: We have to find the derivative  of given expression at point (1, 2)

Q: •T/4 t4 tant dt 2 + cos t -T/4

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Q: (a) Find dy for dx = In (3x – 2) (tan 2x) -

A: Explanation of the solution is given below..

Q: dx Evaluate using x²/x² – 16 = 4 sec(0), where 0 < 0 < . a substitution of x

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Q: cos?t 1. Find the derivative of f(t) :

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

Q: Find T3 (x) centered at c=0.  f(x)=e-x tanx

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Q: Let ä(t) and y(t) be functions of t given as follows • y(t) = t/7, x(t) = cos(t/6). State the…

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Q: Let f (t) = t1ºe1t + e=2t sin 18t. Find L{f (t)}.

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Q: L{sin(T – )µ(T –} 2 2

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