5. Determine the minimum value of f(x) = e* – 3x on the interval [-1,1] [T:3] %3D

Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

Q: Find all the critical points of the function f(x, y) = e" (x² + y³) and determine whether each of…

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Q: 3. Recall that x - Poisson(0) = Mz(t) = e"(e*-1). %3D A. Derive the MGF of Z = (F - 0)/ /0/n where F…

A: Please find the solution below. Thank you.

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: Consider the function f(x) = ln(x)/x^5. f(x) has a critical number A = __? f"(A) = __? Thus we…

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

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Q: If f'(x) = x(x – 5)(x + 1)*, then f(x) has a local minimum at: Select one: а. X = 0 only O b. x = 5…

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Q: 2. Let f(x, y) = (x² + y²)e-. Find and classify all of the critical points.

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Q: Let z be defined implicitly as a function of x and y by the e e-zy əz find O UTM + cos (xy) = (4 –…

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Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

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Q: What is the minimum value of y = 3 + cos 2x?

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: b) If y(t) is the solution satisfying the initial condition y(0) 1, find the value of lim y(t).

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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: 3. Find all the critical points of the function f(x, y) = e(x² + y²) and determine whether each of…

A: Given function is f(x, y) = ey(x2 + y2)

Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

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Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

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Q: 1 1 S(1) = " +. 6r +2 %3D S(r) does not have a global minimum or maximum. What is the value of f(r)…

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Q: 1. Evaluate the limits. e' cos (t – 4) dt - 4 (а) lim x2 x2 – 4 e2 + 2 (b) lim x00 e2x + 100

A: Solve the following

Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

A:

Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: 1 Let H(s) Using convolution to find h(t) s2 (s-a)

A: Inverse Laplace transferom

Q: 5. Suppose f is twice differentiable at xo. If f'(xo) = 0 and f"(x,) > 0, then (a) f has relative…

A: As we know if f(x) is continuous in the domain then and there is a point x= a exist such that

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

A:

Q: 7. Let f(x, y) = In(x)+2 ln(y) – x – 4y. Find the critical point of f and determine if it is a local…

A: Let's find.

Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: 5. Find all the critical points of x + 2 cos x for 0<x<n, and identify each as a local minimum,…

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Q: Find constants a and b in the function f(x): ar In(x) such that f() = 1 and the function function…

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Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: Let = f(x,y) = x² -y. Use Euler's method ( with step size h = 1) to approximate the value of y(2) if…

A: The Euler method is a first-order numerical procedure for solving ordinary differential equations…

Q: 1 3. Integrate the function f (x, y) = over the region bounded by x-axis, line x = 7, and the curve…

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Q: If f(x) has a local maximum at an interior point x= c, then f'(x) exists .a f(x) has a critical…

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Q: (c) Apply the golden ratio search method to locate the minimum of the function f(x) = 4x³ – 20x +…

A: Solution:

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

A:

Q: 2. The Lorenz curve of a particular society is given by L(x) = Ax? + Bx. %3D Suppose that the…

A: We will use given values in Lorenz curve and Gini index to create equations for A and B , Then solve…

Q: Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1

A: Solution

Q: F.M: 15 1. Use second derivative test to classify each of the given critical numbers as a relative…

A: 1. A) f(x) = e-x(x² - 3x + 1)  So, f'(x) = e-x(2x - 3) - e-x(x² - 3x + 1) So, f'(x) = e-x(2x - 3 -…

Q: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

A: You must have an idea about to how to find relative maximum or minimum using critical points.

Q: Find the linearization L(x) of y = e6« ln(x) at a = 1. L(x) =

A: