Let y(t) = e^¹u(t) * Σ d(t-3k). Ž k=16 Show that y(t) = Ae for 0 ≤ t < 3, and determine the value of A.

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A: If , then to determine the meaning of .

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Q: Let f(x) = 2x e¯x*,x > 0 and Let Y x2. Find G(y)and g(y). %3D

A: In this question,  we need to transform the variable in the probability density function.

Q: Let h(x) = 300s a. Find h'(x) and also h'(T/2).

A: The given function is: h(x)=3cos x

Q: aw aw = f(s³ + t²) and f'(x) = e*. Find and at əs Assume that w=f[s]

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Q: 5 3. Let F(x) /t2 17 dt. Find F'(x)

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Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: Find an expression for f (t, p) and evaluate that expression when t = 0. Find an expression for f(t,…

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Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

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Q: Evaluate SIL. dydzdke, where E = {(x,y,z): (2+z12<x< 2, - (4 - z)2sy <(4 -2)12, 3<z 58}.

A: Given: The given integral is ∫∫∫Rdydzdx The given intervals are (y2+x2)12≤x≤2, -(4-z2)12≤y≤(4-z2)12,…

Q: A 2xe ²x² B Xex² Ⓒ2e+² D 2xex² Let f(x)= ex², find f'(x)

A: given  f(x)=ex2d dx(ex)=exd dx(xn)=nxn-1

Q: Q3. Find y= fx) such that y

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Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

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Q: Let h(x) = In[(f(x))² +1. Suppose that f(1) = -1 and f' (1) = 1. Find h'(1).

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Q: Let r(t) = (- Find 7' (t) r' (t) = ( (..) -5 - 2t -3t+3' 5t² - 4 - 3t² -6³-5

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Q: Let h(x) = f(g(x)). If: f(3) = 0, f'(42) = –5, f'(3) = 4, g(3) = 42, & gʻ (3) = 0, then h'(3) =

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Q: 1 Find h' (u). Show your work. Let h(u) = 4u³ – - u?

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Q: Show that Var (Y) = Var(ε₁) = 0².

A: Let us consider a simple linear regression. The equation of a simple linear regression model is:…

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: Let f(x) = e*. What is f' (3)?

A: Differentiate wrt x

Q: ex+1 b) Find f'(x) of f (x) = x2+3 %3D c) For y = xk+1, where k is a constant. Find y'".

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Q: Let 7(t) = FindF (t) 구' (t) - <| Question Help: OVideo Submit Question

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Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: d ch(x) S f(t)dt (x)6xp

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Q: Let f(x) = x°e*. Find f '(x).

A: Product rule:d(uv)dx=udvdx+vdudx

Q: Let 7(t) = Find 7'(t) F'(t) =

A: The objective is to find the derivative of given

Q: Let g(x) = | F(t) dt, where fis the function whose graph is shown. y f 12 1 (a) Evaluate g(x) for x…

A: Given The given integral is  and the given graph is  Apply formula  The area of the right angle…

Q: Let f(x)= $ (x- 3)* k- 4k+1 8. Find: %| k=0 a) f'(x)= b) [ƒ(x)dx=

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Q: 2 DiFferentiate JE F(E) = Sépsx swx + Jbx SK Sinxt XHI と

A: Differentiate Ft=∫t2tcosxsinx+1x+1dx

Q: Let h(x) = x³e" k6*. Find dr (h(x)) wherek is a real number (i.e. k is a constant).

A: Given: h(x)=x3ex3-k6x To find: ddxh(x)