1. Pove that V(X) = E[(X - µ)²] = E(X²) – µ²/ - 2. Prove that E(X + c) = E(X) + c 3. Prove that V(CX) = c²V(X) 4. Let Z = X-. Find E(Z) and V(Z)

Q: Verify that g'(x) 1 where g(x) = v2x – 3. %3D V2r – 3

A: Giveng(x)=2x-3.To verify g'(x)=12x-3  is the derivative of g(x).

Q: Let H(x) = F(G(x)) and J(x) = F(x)/G(x). Suppose F(4) = 9, F'(4) = -7 G(4) = 3, G'(4) = 0 G(-6) = 4,…

A: Given H(x)=F(G(x))H'(x)=G'(x)*F'(G(x))J(x)=F(x)G(x)J'(x)=G(x)F'(x)-F(x)G'(x)G2(x)

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < ¤ < 1 and fx (5) = 5 then E (Y|X = }) =

A:

Q: Let r(x) = f(g(h(x))), where h(1) = 3, g(3) = 6, h'(1) = 3, gʻ(3) = 3, and f '(6) = 5. Find r'(1).…

A:

Q: Let f(x) 11 In(x). Then f'(x) is andf (8) is f"(2) is and f(8) is

A: Use differentiation for finding the values

Q: 4. Let f(x) = e3h(x) and g(x) = h(e3"). Find f'(7) and g'(2) given that h(7) = 2, h'(7) = 4, h'(e) =…

A: We have to find

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(8) and G'(8). = F'(8) = G'(8) = ƒ(8)…

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(9) = 13, f(13) = 3, f'(13) = 12, f'(9)…

A: Given: Let F(x)=f(f(x)) and G(x)=(F(x))2 And f(9)=13, f(13)=3, f'(13)=12, f'(9)=10

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

A:

Q: Use the sample data and confidence level given below to complete parts (a) through (d). In a study…

A: a.

Q: A. If G(2) = F(z) · H(z), then G' (3): %3D B. If G(w) = F(w)/H(w), then G' (3)

A: Given F(3)=1, F'(3)=2, H(3)=4, H'(3)=1.

Q: f'(x) = f'(4) - L

A:

Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x^2+2x−3, what is h′(x)?

A: Given,          hx=fxgx. And fx=-cosx  and  gx=4x2+2x-3.

Q: If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C)…

A: We have to find derivative of f(x).

Q: 8. Find f'(x) for (a) f(x)=(x² +3x+1)(2x+3) 2x-3x+1 (b) ƒ(x)= %3D

A: We need to find the derivative of the given functions. For (a),

Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

A:

Q: 1. Determine f'(x) for each function below: f(x) = x2 – 2x + 3 f(x) = 7x3 · Vx %3D f(x) = x³ In x…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

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

A:

Q: es AB3: Let h(x) = - Find h'(6). 3x %3D 3

A: Here we have,  h(x)=eg(x)3x ....................(1)  we have to find h'(6)=? Now differentiate…

Q: Find a function f(x) such that f'(x)% = - 3a? + 8 and f(0) = 1 f(z) = %3D

A:

Q: 41. Let f(x) = x" and g(x) = x¹/n. Compute g'(x) using Theorem 2 and check your answer using the…

A:

Q: For the following exercises, assume that f(x) and g(x) are both differentiable functions for all x.…

A:

Q: Find the Maclaurin's polynomial of degree 3 for ( a) f(x)=(1+x)e²*

A: Maclaurin Series of f(x) of Degree 3 is : f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(5) = 11, f(11) = 3, f'(11) = 6, f'(5) =…

A:

Q: Show that f(x)g(x) = (x – a)" Cmdn' -m- n'=0 m=0

A:

Q: 17) Let f(x) : Find a %3D X - 9 function y = g(x) so that (f •g)(x) = x. %3D

A:

Q: Suppose that P(A)=0, P(C|A) =0.006, and P(C'|A')=0.0055 Find P(A∣C).

A: GivenP(A)=0P(C|A)=0.006P(C'|A')=0.0055

Q: 3 If f(t)=e3t = f'(t) = 3-s

A: we have ft=e3t we know that  Lft=Fs=∫0∞e-stftdtLf't=sFs-f0So, Le3t=1s-3=Fs

Q: Let f (x) =  x2 − 6 x3 . Find and simplify f ' (x) and f '' (x).f ' (x) =  Ax2 + B xC…

A: The given function is,

Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2

Q: 8. Consider the function f(x) =6x5(x6+10)4 (a) Define u(x) = x6 + 10. Then calculate: u'(x) = (b)…

A:

Q: 4. Prove that: [V(~q(x))] = [3x q(x)].

A: