Suppose E(X) = 2 and E[X(X – 1)] = 28.5. (a) What is E(X2)? [Hint: First verify that E[X(X – 1)] = E[x² - x] = E(x²) – E(X).] (b) What is V(X)? (c) What is the general relationship among the quantities E(X), E[X(X – 1)], and V(X)? O vX) = E[X(X – 1)] – E(X) – [E(X)]? O vX) = E[X(X – 1)] + E(X) + [E(X)]² O V(X) = E[X(X – 1)] – E(X) + [E(X)1² O vX) = E[X(X – 1)] + E(X) – [E(X)1² %3D

Q: (3a) Show that the formula in the Mean-Value Theorem can be written as follows: f(x+h)-f(x) h =…

A:

Q: Given that f'(x) = 4(x + 2)(x + 5), The graph of f(x) at x = 3 is [Select an answer

A: Concept let a function f(x)  and its derivative is f'(x) at x = a if f'(a) >0   ---- then at x =…

Q: (A) (B) (C) (D) (E) What is the derivative of 1 x² + 1 1 x + 1 1 √x² +1 X x² +1 2x x² + 1 f(x) =…

A:

Q: Let g(x) be the inverse of f(x) = x³ + 5x + 2. Note that f(1) = 8. Calculate g(8), without finding a…

A: Given that g(x) is inverse of f(x)=x3+5x+2,  and f(1)=8

Q: Suppose f(x) is the function such that for a > 0 we have f(x) = (e" – 1) In(x) and for x < 0 we have…

A:

Q: 3. (a) (10) Let g(x) Find g'(x). Don't try to simplify your answer. In(4.x) – cos(2x)

A: Given function g(x) is differentiate w.r.t x as written below:

Q: Given that f(x) = 8x (a) f(g(0))= (b) g(ƒ(0))= - 6 and g(x) = 6 x², calculate

A: f(x)=8x-6g(x)=6-x2

Q: If g(x) + x cos(g(x)) = x8, find g ′(0).

A: In order to calculate g'(0) we first need to find out g'(x) by differentiating the above given…

Q: Suppose E(X) = 4 and E[X(X − 1)] = 22.5. (a) What is E(X²)? [Hint: First verify that E[X(X − 1)] =…

A: Ans#- Suppose E(X) = 4 and E[X(X - 1)] = 22.5           (a) Find E(X2) =?           (b) Find V(X)=?…

Q: Consider the function f(2) = 4z + e* +5 with g(z) - f-' (z). (a) Show that f(x) in ne-one on R. (b)…

A: (a) From the definition of one to one function, if there doesn't exist such y in its codomain such…

Q: (a) f(x) = (2x – 1)*(3x – 2)³ (b) f(x) = [(x – 3)(5x + 1)]³ (c) f(x) = Vx cos ((3x + 2)²) %3D CoS…

A:

Q: Given that h(x) = f(g(x)), use the graphs of f(x) and g(x) to find h'(3). -0.5 [A] 0 3.5 3 2:5 2 1.5…

A: Given that h(x) = f(g(x)) The graph of f(x) and g(x) is given as

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

A:

Q: Suppose that for all real x S'(x) = -g(x) and g'(x) = f(x). (a) Show that f²(x)+g²(x)= C for some…

A:

Q: Consider the functions: h(x) = f(g(x)) and Use the graphs of f(x) and g(x) to find the following •…

A:

Q: 2. Use chain rule to find the derivative of the following functions (Hint: for function composed…

A: NOTE: Refresh your page if you can't see any equations. . Since you have asked multiple questions,…

Q: functions identical?

A:

Q: Suppose E(X) = 4 and E[X(X – 1)] = 25.5. (a) What is E(x2)? [Hint: First verify that E[X(X – 1)] =…

A: Given: EX=4EXX-1=25.5 So, a) EX2-X=25.5EX2-EX=25.5EX2=25.5+4=29.5

Q: Solve y = (1 + y) sec (x) + tan (x) a. y = (x + c) [sec (x) + tan (x)] b. y = (c x) [sec (x) + tan…

A:

Q: 1. Find the derivative of the following f) y = (2x − 1) ( x³ − x) + √x[2(x³ − x) + (2x − 1)(3x² −…

A:

Q: Suppose E(X) = 5 and E[X(X-1)] = 24.5. (a) What is E(X²)? [Hint: First verify that E[X(X - 1)] = [X²…

A: It is given that  E(X) = 5 E(X(X-1)) = 24.5

Q: If* f(x) = xe, then Newton's formula has: (A) Xn+1 (B) Xn+1) (C) Xn + 1 (D) Xn + 1 Xen Vehicle-1…

A: