Question 9 Let f(t) be a continuous function for t20 and F(s) = f(t)e dt. Select all that apply Your answer: The integral ele"dt converges to 0. for s>9 O The integral 7e "dt converges to for s>0. The integral cos(7t)e dt diverges for all s.

Q: Find f. 8. f'(t : f(1) = 0 1+2' f(t) =

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Q: Suppose that for each i such that 1 <i<N one has / f(1)dt = i Ji-1 What is / f(t)dt if N = 87?

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Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

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Q: 4 3 2 1 y 1 y = f(x) 2 3 4 -X

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Q: For the function f(t) graphed at the right, let g(x)=| f(t)dt. Find :a) g(-4); b) g(3); c)g'(3) f(t)

A: Consider the graph of function f(t)

Q: 2 2et 5 Let 7(t) 5, Evaluate the definite integral. %3D 13 | F(t)dt = ( 6.

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Q: Apply Parseval's identity to the function f (x) = x, - nSxSn and deduce that n16 = 1/12+1/22 + . +…

A: For the solution follow the next steps.

Q: If f is continuous and f(t) dt = 18, find the integral Answer:

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Q: t F(x) cos(3t – 1) dt sin z %3D

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Q: Let F(æ) = | a cos(3t – 1) dt. sin a 1. Find F(0). 2. Find F'(x).

A: F(x)=∫sinxx2cos3t-1dtPut 3t-1=udifferentiate w.r.t t3dt=duput t=sinx then u=3sinx-1if t=x2 then…

Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

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Q: If x € (0, 2) then compute ( f 2 7) ² dx. x x cos x-sin x

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Q: Suppose that f is a function defined as f(r) = | (+4)dt . Find each of the f(1) = f(x) = f'(r) =

A: Answer and explanation is given below

Q: The graph of the function fis shown on the right. a. Evaluate , f(x) dx. Let A (x) = f(t)dt. b. Find…

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Q: A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some…

A: Since derivatives of F(t) represent the rate at which the fraction F(t) of burnt out bulbs increase…

Q: 5. Given F(x) = cos (t) dt, determine F'(x). 2

A: Using leibniz rule  Explanation is given below....

Q: 7. If f is a continuous function such that f(t)dt = x sin x + f(t) dt for all x , find an explicit…

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Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: Which of the following finite difference scheme can be used to estimate the first derivative?

A: The finite difference scheme is an approximate method of getting the solution of  partial…

Q: = 1₁²₂ x 3. Define F(x): 1 /1+t² dt. Find F(8) and F'(8).

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Q: P c=0 and I= 1. d (a) Use the definition of the derivative to prove IP d. -I" = nr"-1 for all n E…

A: Given , Function =xn To Prove :ddxxn= nxn-1  using Quotient rule

Q: Differentiate the following function: (e-*) * y = sec

A: Given: y=sece-x2

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: Use the Runge-Kutta(2) with h=2 to approximate x(4) for the IVP x'=x?-t+1, 23154, x(2) =2. OA 31 O…

A: Use Runge-Kutta 2nd order with h=2 to approximate x4 for the IVP         x'=x2-t+1,       2≤t≤4x2=2…

Q: II. Let F(x) = | cos(3t – 1) dt. - sin 1. Find F(0). 2. Find F'(x x).

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Q: Let g(x) = xe² and f(x) = f g(t) (t+1/t)dt. Which of the following is closest to the value of Select…

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