E[X]E[l/X] > 1, if X > 0, E[X] < o, E[1/X] < co. O True O False

Q: Consider the following functions. f,(x) = cos(2x), f,(x) = 1, f(x) = cos²(x) g(x) = c,f,(x) + c,(x)…

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Q: [3 – e -kl – cos x + log(x²)]dx = 0

A: Given,∫a5 3-e-x-cos x+log x2 dx

Q: Let f(x) = cos (x). %3D If it is true that f" (x) = x(f'(x))ª for some constant a, find the value of…

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

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Q: How many of the following are valid functions? f: R→R, f(x) = e = g: R→ R, g(x) = ln(x² + 1) h : R →…

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Q: f'(2) for (x- x)(x² +2)(x² +x- 1) S(x) = %3D x + 2 O 676/5 O 379/7 O 587/3 O 384/9 O 585/4 O 699/7

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Q: Find the characteristic function for fy(x)=e.

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Q: (2) Show that f(x) = e³x cos(2x) is of exponential order.

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Q: 周 紀 =xlogæ+O(x).

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Q: If there exists a normal line at (a, f(a)), a E R, then f' (a) is defined. True False

A: We have given  There exist a normal  line at a,fa As slope of normal line is given as m=-1f'a For…

Q: Consider the function H(x)=cos(e* +5). If we write H as a composition H(x)= f(g(x)), what can f(x)…

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Q: Let f(x) = 5x², c= -1, Find a value 6 > 0 such that 0 < L = 4, and & = 0.3. x-cl < 8⇒ f(x) - L| < E.

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Q: Let X ∼ Gamma(α, β) for α > 1. Find E{1/X}. How does this compare with 1/EX?

A: Given that the random variable  follows a Gamma distribution with parameter  and .Its probability…

Q: Determine E (X) and V(X) x -1.0 -0.5 0.5 1.0 a. E(X) = 1/8 V(X) = 0.4219 b. None O c. E(X) = 0 V(X)…

A: E(x) = (-1 x 1/3) + (-0.5 x 1/6) + (0.5 x 1/6)             + ( 1 x 1/3)        = (-1/3) + (-1/12) +…

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: Prove that for x > 1, (x − 1)/x< ln x < x − 1.

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Q: Find the function of the form y = loga (x) whose graph is given. y = y 1.5 1.0 0.5 -0.5 -1.0 2 4 6…

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Q: Given 1/3 ≤ x < y ≤ 3, prove that |ln y − ln x| ≤ 3|y − x|

A: Consider the given inequality ln y-ln x≤3y-x, 13≤x&lt;y≤3 Consider x=12, y=1 Then ln 1-ln…

Q: > log æ – - log2+y=tan + x Y ○ 2(1 − x)x+ 2x² = 3x - 1 - ○ (3x − 1)(2x + 1) = 0 O sin(y) + e*² = 5y

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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).…

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Q: Let g(x) = kf(x) for all x E/= {x: asxsb}. Show that Jglx)dx = kJ f(x)dx if k<0.

A: To prove the above result we use the definition of lower and upper Riemann integrals. For the proof…

Q: - Find E f(x) dx if [3 for x 3 f(x) =

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Q: 2- Find the Root of the function F(x) = e*(3.2 sin(x) - 0.5 cos(x)) Using XL=3 , X,=4 , ɛs = 0.002

A: Let f(x)=e-x(3.2sin(x)-0.5cos(x))…

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: 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: |In² x – 4 ln x – 5| Evaluate - dx. e-3

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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: Suppose X Poi(X) for some positive X. a. Show that E(X) = X b. Show that E[X(X - 1)] = X².

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Q: Let f(x) = 3 + 2(x-3) + 0(x-3), as x→3 and let g(x) 2 B. g (3) = ² 3 ·g is defined and…

A: We will find the required.

Q: Let f: R Rwith f(z) = e. Which one of the following functions is equal f(z)? O log10(z) O log2(z) O…

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Q: 2- Find the Root of the function F(x) = e*(3.2 sin(x) - 0.5 cos(x)) Using XL=3 , X,=4 , Ɛs= 0.002

A: This is to be solved by successive bisection method.

Q: x2 - 1 x² + 1 17. tanh(ln x)

A: We have to prove the given identity

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…

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Q: dx хӀn(х) 1. Vy3 5 secx tan³x ||

A: Given that  1.y35=x lnxsecx tan3xfind dydx

Q: 1. Prove that (i) Log i = 2 (ii) Log(-5) = ln 5 + ti %3D i) = 3 In 2 + 2 (iv) Log(1+i) = In 2 + 3ri…

A: Since you have posted multiple questions, we will solve only first three parts of first question for…