Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

Q: For the following systems, find th

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The function f:R→R defined as fW)=log_lV\x²+1+x+VVx²+1-x) is

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Q: Then the value of E(g(X)) is:

A: The E(g(X)) can be calculated as E(g(X)) = E(4 X + 3) = 4.E(Xhh) + 3

Q: Let X - x? (s): (a) find E (X² +2x) where E (g (x)) = 6° g (x) fx (x) dx. %3D (b) find the…

A: Given

Q: Alog f(x) = log[1+ Af(x), f(x)

A: We have to solve given problem:

Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

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Q: Find the indefinite intergral of 1/(e^x -1)

A: To Find the indefinite intergral of 1/(e^x -1)

Q: 62. a. Show that e>1+x for x > 0.

A: We will answer the first question only as those all are different and we don't answer multiple…

Q: Find for the function y = In 20 1+ e

A: The given function is y=lnet21+et2. Chain rule: ddtfgt=f'gtg't Quotient rule:…

Q: Find g' (e) if g(x) = In(2x + e³).

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Q: x • e e- for x <x < ∞ f(x) elsewhere

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Q: Expand g (x) = e-³* in powers of (x + 1). (-1)**'e°(x + 1¥ а) k! k=0 (-1)*e³5*cx + 1)* b) O2 k=0 k!…

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Q: Q1 Find root of equation f(x) = In (x')-5, using N-R method in [5,6] with e S0.0001, take E=|x1-x,…

A: Note: It is assumed that the N-R method is the Newton-Raphson method. The root of the equation…

Q: s evaluate e of 1. The

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Q: = x3 + x - rith starting d with the of x after the

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Q: 1. Employ Bairstow's method t

A: f(x)=9.34-21.97x+16.3x2-3.704x3Initial guesses of r=1, s=-1 and…

Q: Find E[X-E[X]]]

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Q: . Find the exact values of the six circeular functions of e.

A: Six circular functions of 'θ' sinθ,cosθ,tanθ,cscθ,secθ and cotθ According to the question, First…

Q: and the range is The exponential function f with base b is defined by f(x) = , b>0 and b 1. Using…

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Q: (b) Use the iteration formula 4(3-х,) (3+x,) with x, = 1 to find, to 2 decimal places, the value of…

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Q: 4. f (x) = log2 x and g(x) = vx – 4. What is the domain of f( g(x))and g(f(x))?

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Q: The Gini index, given by 2∫10(x−f(x))dx2∫01(x−f(x))dx, is a measure of a country's income equality…

A: 2∫01(x-f(x))dx    , f(x) = x5.3

Q: Find, to three decimal places, the value of x such that e−x = x.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find f’(e) of the following function. f(x)= x3 *(ln x- 1/3)

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Q: Graph the function f(x) = u₂(x) ln x + u₁(x) (ln(10 − x) - ln x)

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Q: Find a general formula for f^n. f(x)=7x^2 e^x

A: Consider the given function fx=7x2ex. In order to find the nth derivative f'n, differentiate the…

Q: For any n large enough, prove E" ) – = 0(1). k=0

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Q: The function f(x) = X = (6x 3) e5 has one critical number. Find it.

A: Given function ,   f(x)=(6x-3)e5x

Q: Find the domain of the function. g(x) = ln(x - 1)

A: A function is a relation between an input variable and an output variable wherein each input…

Q: Given the functions f(x) = log₂ (2x) and g(x) = 2x - 3, which of the following statements is true?…

A: Here, the given functions are f(x)=log2(2x) =ln (2x)ln 2(used change of base)&amp; g(x)=2x-3 Here,…

Q: Using OLS or any other suitable method, Prove that E(ß1) = B1

A: Full form of OLS estimator is ordinary least square method. β^1 is the parameter of the model. Under…

Q: Find a formula for f(n)(x) if f(x) = e' -3x fln)(x):

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Q: and X4 %3D If the engine type is traditional, then x3 = When you plug in these two values in the…

A: When the qualitative predictor has m levels then we create (m-1) dummy variables. Here the…

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: *x-x' +x* -x' and |x|<0.2. 1+x Find the upper bound on the error if

A: Given : x1+x2≈x-x3+x5-x7 and x≤0.2 To find : upper bound on the error of the given Maclaurin series…

Q: X-1 e e-1 +X xp- e*+x°

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Q: Calculate the residue of e.e5=0

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Q: Find the range of the function x* +e x+e f(x)%3sin{log, +cos {log. x' +1 2 x*+1

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Q: (x) = ln(1 + e8x), find f '(0).

A: Given,          fx=ln1+e8x

Q: Find f'(x) of each of the following functions. (e) f(x)=e* In(x')

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Q: For a general L(x), demonstrate that G = 1 - 2B. What range of values does the Gini index occupy?

A: For a general Lx, the Gini index G is, G=AA+B    ⋯⋯(1) Also, from the above tabulation, G=2A From…

Q: Find y''of 4cos(x/2)+e^-2x

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Q: Find the domain: g(x) = ln(e^x -5)

A: The domain of ln z is z&gt;0. We'll use the same concept here. So e^x-5&gt;0.

Q: Then the value of E(g(X)) is: is:

A: here given pdf of x  here g(x) = 5X

Q: If ƒ(x) = ln x and g(x) = 4 - x2, find the functions ƒ ∘ g, g ∘ ƒ, ƒ ∘ ƒ, g ∘ g, and their domains.

A: It is given that f(x) = lnx and g(x) =4 – x2.

Q: g(x) = e× In x12 g'(x)=

A: topic - derivative of a function

Q: x = y + Z y² = 0.000396707 - 0.24576 x2 z* = 0.00029753 – 0.12288 x²

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Q: Find E if E = x• P(x)

A: Our aim is to find the