The moment generationg function of X is defined by M(t) =Var(etx) ylgn ihi

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: 4. Let A(x) = ſ dt. Find the local minima, local maxima, and t2+1 inflection points of A(x).

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Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: Let X ~ Poisson(λ). Derive the moment generating function of X and use that to find E(X3)

A: Solution: Let X~Poisson(λ) The probability distribution of X is  P(x)=e-λλxx!    x=0,1,2,3,..

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval. y = √x, [9,…

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Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Find the Hessian of the function. Based on result in c), determine the types of stationary points…

A: We need to find the Hessian and stationary points of the function f(x,y)= x3+y2-2xy.

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

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Q: Find the MRSxy of the utility function U=In(x)+y.

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Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: Find the linearization of the function given below at the specified point. f(x) 4 In(x) at a = 1…

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Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

A: The function f(x)=2 cos 2x on the interval 0,π

Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: frod ll Critical points on the fcx) = x² Jq-x² 2. curve f(x)

A: Solution:- Critical point:- critical points are point where the function f(x) is defined and its…

Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: Find the orthogonal trajectories of the following family: y = Ce-x

A: First differentiate then  solve

Q: Find the linearization L(x) of y = e5* In(x) at a = 1. L(x) =

A: Given that:y=e5xln(x)a=1To find the linearization

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

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Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: Bi(n, p) and using the MGF compute Derive the moment generating function of X E[X] and Var[X].

A: Given,A random variable X~Bi(n,p)P(X=x)=nxpxqn-x    ;   X=0,1,2,.....nand q=1-p

Q: The moment generating function of X is defined by M(t)=E(etx) صواب İhi

A: True.

Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

A:

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

A:

Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: Let Dx be the linear transformation from C'[a, b] into Cla, b]. Find the preimage of the function.…

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Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Solution: Consider the given linear transformation : Dxf = 2x + 3 Since D is the linear…

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: if the implicit function is x3=at2, find the d2x/dt2

A: if the implicit function is x3=at2, find the d2x/dt2

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: A function y(t) satisfies th

A: Given, the differential equation                       dydt=-y4-3y3+4y2

Q: a Find the Orthogonal trajectories of the family of r =; 1+coso

A: we need to find the orthogonal trajectories of the given family of the curve in the polar form.

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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

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Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: Let T be a statistic, then T is sufficient statistic for 0 if the conditional pdf f(0,x1, X2,..…

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Q: 8. Find the orthogonal trajectories of y cx

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Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

A: