Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2 are independent, then X2~ X- %3D

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

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Q: り If X~メ (2)、 Find the 32-moment of x about zero

A: Introduction: The random variable X has a chi-squared distribution with 2 degrees of freedom, that…

Q: Find the linearization L(x) of f(x) at x = a. f («) — 4а? + 2а — 3, а — -5 -

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Q: Use Cauchy's residue theorem to evaluate the function f(z)

A: Let C is the circle z=2 oriented counter clockwise (in the Positive sense). Then the function…

Q: a) Find all critical points of the function f(x,y) = x³ + 3y - y³ - 3x and classify them as local…

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Q: Find the linearization L(x) of f(x)=tan x at x=3pie/4.

A: Given

Q: Prove that y = x- 2 is differentiable and calculate y'.

A: Given: The function, y = x-2

Q: : Jhat is he nodies onuegence

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Q: Find linearization L(x) of f (x) = Vx at a =4 and use to approximate 7.8.

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Q: Identify the equation of the normal line of the funtion f(x) = -3x at x=2

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Q: 1. Determine where f(x) = arcsin (x² – 2x) is increasing. %3D

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Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: Use the definition of the hyperbolic functions to prove that 2cosh (x)-1=cosh(2x).

A: As per the instruction, we will be answering only the first question. For (a),      2 cosh2(x)-1=2…

Q: show steps please

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Q: Evaluate divergence VA when A = 2xay + 3yay- 4zaz and V = xyz.

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Q: The moment generating function is always exist

A: The moment-generating function of a real-valued distribution does not always exist.

Q: Let F (x) = %3D In tdt then F' (x) = et3

A: To find F'(t)

Q: Find the linearization of the function at a . f(x) = sin x    , a = pie /6

A: The given function fx=sinx, a=π6

Q: Calculate facterial funchion n -X x e %3D

A: Using integration by parts solve the integral:  ∫0∞xne-xdx=∫xne-xdx0∞…

Q: Draw the y = sinx and y = 1- x² on the domain -2 <x<2 and filling the between the funtions.

A: the filling part is given below-

Q: Find the linearization L(x) at x= a. f(x) = 2x° + 5x - 3 a= 3 L(x) =

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Q: Find the linearization L(x) of f(x) at x = a. 3 6) f(x) = x, a = 8 %3D

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Q: attached

A: Linearization of f(x) at x=a is given by

Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Find the intervals of convexity/concavity of the functionf(x)=x−cosx.

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Q: GrRve the domnin f n(x)= -9-4x|usq iaeoul.ntaton

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Q: For what value of x does the funciton g(x)= (1/3)x^3-2x^2 strictly convex?

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Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: Find the linearization L(x) at x = a. f(x) = - 4x3 - 3x+1 a = - 3 L(x) =

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Q: Let f: A→ B, where A= {1,-1}, B= {1,2,3}, and f(x)= 3×x²+2, find Range إجابتك * Codomain إجابك * Is…

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Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: D2 – 4)y = 10e-3x + 6e2x

A: Given: D2-4y=10e-3x+6e2x The auxiliary equation is: m2-4=0 Now solve; m2-4=0m2-22=0m+2m-2=0m+2=0 or…

Q: Consider an F-curve with d f = (2, 14). Identify the degrees of freedom for the numerator.

A: The degrees of freedom for the F-statistic is df=(k−1, n−k).

Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: 3. 4. S 2t (1²+2) ³ 514 √15 +2 - dt =dt

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Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

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Q: Find the Wronskian for the set of functions.{x, −sin x}

A: Given:  f(x1)=x and f(x2)=(-sinx ) The wronskian is given by the following determinant:

Q: Find the linearization L(x)of the function at a .

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Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: Find the linearization L(x) of f(x) at x = a. f(x) = a = 0 4x +3

A: topic - linearization of a function

Q: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the same set of…

A: To Determine: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the…

Q: 2. Use the Intermediate Value Theorem to prove that the equation e* = 4 - x³is solvable on the…

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Q: Fix a constant r>1 Using the Mean Value Theorem that enx > 1 + x for any fixed x >0 prove

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Q: Determine local extremum f(x,g) = xy(4-x-). %3D

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Q: Find the solutim and define the interval at which func tien is depime dx

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Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…