Show that E[X]= a +V and o = b 4 4 -

Q: If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.

A: To compute y'

Q: Let f(x) = cx3.8 and suppose that f(2) = 16. Find the value of c.

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

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Q: Use the elimination method to find a general solution for the given linear system, where…

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Q: If f(x) = x + /2 – x and g(u) = u + v2 – u , is it true that f = g?

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Q: Let f(x) =x²-x -5 and gx)= -8x+4. Find g(3) and f(g(3)). %3D 9(3) = f(g(3)) = %3D %3D

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Q: If f(x) ' (1 ) cos (x)

A: We have f(x)=xcosx. So,            f'(x)=xcosx'            =xsecx'            =x'secx+secx' x…

Q: Show that an = 1/2n + 1 is decreasing.

A: Given: an=12n+1 Substitute 1 for n in the equation an=12n+1. a1=12(1)+1=13=0.333

Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

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Q: 1.8 If f(x) = -7x – 6 and g(x) = -8x² – 4x + 3, find g(f(3)). a. 393 b. -177 С. -1857 d. -279

A: Here I am attaching image so that you understand each and every step. Given answer option "C" match…

Q: J1(z) rove that J(x) = -J(z) and J{(r) = Jo(z)- %3D

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Q: If f(x) = 5x + In(x – 2), find f15) A. OIn 13 В. C. O5 D. IC

A: Given function is f(x)=5x+ln(x-2) Let f-1(15)=a. Then f(a)=15 Now just check all the options one by…

Q: Calculate R8 for f(x) = 9 - x over [3, 5]. R8

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

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Q: Find the derivative of the function. Ax) = 6x (9 - 8x)* O (- 12x) (9 - 8x)' (6x- 9) O (-181 )(9- 82)…

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Q: Let f(x) = cx4.2 and suppose that f(5) = 30. Find the value of c.

A: Given f(x) = cx4.2

Q: (d) Are X1 and X2 independent? Justify. (e) Compute E(X1) and V(X1).

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Q: Let f(x) 1 and g(x) = 4x + 7. Then с — 3 - (f o g)(0) = (f o g)(x) =

A: Given:

Q: Compute P(X) using the binomial probability formula. Then determine whether the normal distribution…

A: Given: n = 42 p = 0.6 q = 1-p = 1-0.6 = 0.4 q = 0.4 Formula Used: Probability mass function of…

Q: Consider the function f(x) = Ax³ + Bx² + 5x. Find the values of A and B if f'(-2) = -3 and f" (-2) =…

A: f(x)=Ax3+Bx2+5x

Q: Let f : R → R, where f(n) = 5 . Answer the following questions. 7x²+3*

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Q: Find the following. Let f(x)= x+1, g(x)= 2x, and h(x)=x-2. a. (h o h) (x) b. (f o g) (x) c. (g o h)…

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Q: 2 Suppose y is a function of x such that y * and y(4) = -3. Find y. |

A: The differential equation is given by y' = 2x                                   .......(1) Initial…