Calculate E((X +Y)²).

Q: Sze*2dx = 1. This is a difficult integral to compute by standard methods (there's a neat trick…

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Q: Determine p′(x) when p(x)=0.08ex / √x.

A: Given 0.08ex / √x expression we need to find its integral.Let us substitute √x = u and we get du/dx…

Q: y = x lnx,  [1,2]

A: MVT conclusion for point ‘c’ is

Q: Find ∫√(2x − 1) dx.

A: Given:

Q: Find  f ′(a)  f(x) = 2x4,    a = −1

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Q: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A:

Q: Show that (A − B )T = AT − B T .

A: Given  (A − B )T = AT − B T

Q: A discrete random variable Y is such that 1 y(y + 1)' P(Y = y) = y = 1, 2, 3, ...

A: Given:Y is a discrete random variable.P(Y=y)=1y(y+1),       1,2,3,.....Find:E(Y)

Q: Find the linearisation of f(x) = 4√x at a = 16. Use this to estimate 4√ 15

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Q: dæ = -L/R+ x dt

A: Note: It is assumed that R is a constant. Follow the steps below to solve the given differential…

Q: a. Find Dx ​( f [ g ( x ) ] ) at x = 4. b. Find Dx ​( f [ g ( x ) ] ) at x = 2.

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Q: Let f(1) = 2 and f (1) = 3. Suppose g(x) = [f(x)²=]. Calculate g' (1). %3D %3D

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Q: Rewrite the given function F(x) dt as %3D F(x) %D -2t dt.

A:

Q: a. Find E(X) b. Find E(Y) c. Find E(XY)

A: a.The joint probability density function is,

Q: Find ∫ dx/√(e2x − 1)

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Q: Suppose Find the value of f(10). f(10) = _. d _ƒ(x) = 6x, f(1) = 8. dx

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Q: Determine y′(7) to the nearest tenth when y(x)=50x4 / 2x (Do not include "y′(7)=" in your answer.)

A: We have to find derivative of y at x=7.y is given below:

Q: Find | [3f(x) – g(x)]dx : i if 6 f(x)dx 2 and g(x)dx = 30 %3D %3D

A: Given: I=∫163fx-gxdx And ∫16fxdx=2 ; ∫16gxdx=30 We know that; the sum rule: ∫fx±gxdx=∫fxdxdx±∫gxdx…

Q: Show that esin(x²)dx < e– 1.

A:

Q: f (x) = x5, x = 1/2

A: The function is given as fx=x5

Q: Determine r′(8) to the nearest tenth when r(x)=90x5 / 2x (Do not include "r′(8)=" in your answer.)

A: We have to find derivative of r(x) at given point.r(x) is given by:

Q: etermine the intervals where the function f(x) = x 2 e −x is increasing and where it is decreasing

A: Determine the intervals where the function f(x) = x 2 e −x is increasing and where it is…

Q: If h(x)=6ex−5, find h′(x).

A:

Q: Determine the value of x for which f(x) = x³9x² + 5x-e7 +11″ has the lowest instantaneous rate of…

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Q: Find f. f ″(x) = 8x3 + 5,    f(1) = 5,    f ′(1) = 4

A: