Let X be a positive random variable; i.e P(X ≤ 0) = 0. Which one is correct? (1) E (+) (²) (11) E[log(X)] ≥ log[E(X)]. (III) [E(X)]³ ≥ E(X³). (IV) None of the above. O (III) O (II) O (IV) 1 ²(X) O (1)

Q: Which of the functions g(x) are such that 4" is (g(x))? (Select all that apply.) Og(x)=2+3+4 Dg(x) =…

A: Solution 5 : the correct options are : A and E Solution 6 : the correct options are : A

Q: 1. Which of the following is incorrect? a. b. [(f(x) · g(x)) dx = [ f(x) dx . [ g(x) dx [(f(x) +…

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Q: 9. Select the function that matches the table of values. -3 -2 -1 0 1 2 3 y 23 8 13 4 SIN 5 2 4 1 7…

A: Consider the given table :

Q: Use the following table of values to answer (a) and (b) a)  Let h(x) = f (g(x)) . Find h'(2) .…

A:

Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

A:

Q: (d) In 3 – In x – In(x+ 5) = 0 (f) log2(x – 1) – log2(x+3) = log2 ) (e) log,(x + 2) – log,(x – 1) =…

A: Given d ln3-lnx-lnx+5=0e log4x+2-log4x-1=1f log2x-1-log2x+3=log21x

Q: - 3. Show that if y = ln (-¹), then -1 V'(x) = { Hint: Recall that the domain of the natural…

A:

Q: Y Let A(x) constant, is a solution of (x³ - x) dy dx +x Then, A is = = log x + C Where C is an…

A: Given yA(x)=log x+C, where C is an arbitrary constant, is a solution of (x3-x)dydx-(3x2-1)y=x5-2x3+x…

Q: 周 紀 =xlogæ+O(x).

A:

Q: Solve the following. If f(x)= n# -1, then f'(x)= n+1 >

A: We can solve it using the properties of differentiation as below

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: For all x 1 we have

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Q: 22 Find f(3x + 1)dx if f(x)dx = 1. 10 Enter the exact answer. f(3x + 1)dx =

A: See the solution.

Q: If f(x) = cos (x) and f(a) = find the exact value of the following. (a) f(-a) (b) f(a) + f(a + 2t) +…

A: Solution)a) f(x) = cos x f(-a) =cos(-a)= cos a f(a) = cos a = 1/6 Hence answer is 1/6 b) f(a) +f(a…

Q: Given f (x) = 3x + 2 – 1, what is f –1(x)?  f –1(x) = log3(x – 1) + 2  f –1(x) = log3(x + 1) – 2…

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Q: The derivative of f(z) = Log(2iz - 4+ 6i) at z = -3+i is Undefined. O None of them О —1 3 Log(-6).…

A:

Q: Ex. 17 The value (1+ x) of ] x (1+ xe*)? dx, is equal хе 1 + C (1+ xe*) (a) log + 1+ xe* xe* 1 (b)…

A:

Q: 1+x2 Through the proof of the logarithmic form of the function y-cschx-In(- |x| which of the…

A: The logarithmic function is the inverse function of the exponential function. The logarithmic…

Q: Σlogp pa P = xlogx + O(x).

A:

Q: Let f(x) = x and g(x) = log₁ x. Find [f(x) • g(x) dx (A B d dx -[f(x) • g(x)] d dx =[f(x) • g(x)] =…

A: Given; f(x)=x and g(x)=log5x.

Q: hy's mea x) = eX

A:

Q: 3. (a) Use Tables, or otherwise, to evaluate Simplify your answer. (b) Use a u-substitution to…

A: As per bartleby guidelines we only give first question answer. Please repost for other parts.

Q: 1.4 If f(x)=(2x+2)(x+3) and g(x)= 4x+3 1.4.1 For which value of x is f(x)be non- real? 1.4.2 Solve…

A: The given functions are: f(x)=(2x+2)(x+3)=2x2+8x+6g(x)=4x+3

Q: The function f(x) = cos (e* + e¯x) + x is... O even an exponential function. O odd both even and…

A: Solution:      f(x) = cos (ex + e-x) + x     Now, f(-x) = cos (e-x + e-(-x)) + (-x)…

Q: a) Given a surjective function f : [-1, 1] → [-1, 1], prove or disprove: f-l (f{0}) = {0}. b) Find…

A:

Q: to get from E[X-E (x)] ² the steps. Show how to E[x²] - [E(~x)]². Show

A:

Q: (a) Show that e>1+ x if x> 0. [Hint: Show that f(x) = e* – (1 + x) is increasing for x> 0.] (b)…

A: If x≥0 as exp is increase we have ex≥1. they by means value theorem there exist c∈0,x such that…

Q: S ³f(x) dx = 5, ³g(x) dx = 7, and Which of the following can be determined given Ⓒ S (f(x) - g(x))…

A: We have to solve integral

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: f'(x) for f(x) = 10840 d - a. 1 (In 4)(x + 1) b. 6x5(In 4) x6+1 C. 6x5 + 6x°

A:

Q: (a) Approximate the value of In(2) by (i) using z = 1 in the Maclaurin polynomial of degree 3 of…

A: The aim is to approximate the value of ln 2 using (i) x=1 in the Maclaurin polynomial of degree 3 of…

Q: Let f(x) = ex-1 + 5 ln (x) + 4x. You may assume that f(x) is one-to-one. What is f-¹ (5)? (Your…

A:

Q: In n (4) {} (e) {E 5Vn + Vn J

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Q: or the fucntions f(x)= log 1/2 (x)and g(x)= log 1/16 (x) where is f>g and g>f

A: The given functions are: fx=log12xgx=log116x We have to find the intervals where f>g  and…

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