Let S = {(x, y) :x² + (y – 1)² < 1} U {(3,0)}. %3D Is the origin an extreme point of conv S? Is the origin a vertex of conv S?

Q: (a) Show that y for the given z = e" In x+ xy

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Q: Given the first-order ODE dy -12y , dt Perform a linear stability analysis to find the amplification…

A: Given, dydt=-12yTo find: Amplification factor for the mid point method applied to given ordinary…

Q: Find the maximum likelihood estimates of t when f(t) = (1-t)l-k tk for k-0, 1

A: We have a discrete distribution function given by ft=1-t1-k.tk for k=0, 1  t is an unknown…

Q: f(x) = 13x- In(7x + 14) %3D has a single critical number at x = A. Find this critical number. A =…

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Q: 10- Find a and b in y-a.cos bx using the nonlinear least square method to fit the following data (bx…

A: Given that: x 0.1 0.3 0.5 0.7 0.9 y 0.68689 0.60040 0.43513 0.21407 -0.03443 The objective…

Q: - Find the antiderivative, FCx), and Check your answer of the funetionçiven xZ+3x+5 by f (x)=

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Q: Find the values of x,y and z using Gauss Jordan method.

A: We have given a system of equations ,  3x + 4y + z = 102x - 3y + 5z + 9 = 0x + 2y - z = 6 This…

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: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

A: We have to show if z0 is an isolated singularity of f(z) that is not removable, then z0 is an…

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: The number of defects on the front side (X) of a wooden panel and the number of defects  on the rear…

A: Here, fXY (x, y) = c(x+y) Joint Distribution of X and Y can be formulated as: X\Y 1 2 3 Total of…

Q: The Wronskian 1. Show that the functions ex, cos x and sin x are linearly independent.

A: As per guidelines, We’ll answer the first question since the exact one wasn’t specified. Please…

Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: 6. Let 1 f (x) - cos x + sin(2x), x E [0, 1] 2 Find the least squares polynomial approximation of…

A: Let fx=12cos x-sin2x, x∈0,1. To find quadratic fitting  fx≈P2x=a0+a1x+a2x2 Consider, s0=∫011dx=1

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: -8 6. Evaluate the integral +y² dydx

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Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Let p(x)= e5x be the standard integrating 3 factor to x y' +p(x)y =x°. Find p(8).

A: We have to find the value of p(8).

Q: What is the Wronskian for y" + 3y = In x? & W 3 b. W = 3 c. W = V3cos 3x-V3 sin V3x d. W 3 cos 3x -3…

A: Here, the characteristic equation is m2+3=0. So,                         m2+3=0⇒m=±3 Thus, the…

Q: Find solution of an equation x X f(x) 1 1.0000 1.25 0.8000 1.50 0.6667 0.5714 1.75 2.0 0.5000 Using…

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Q: ==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

A: The Stoke's theorem states that ∫CF·dr=∬S∇×F·dS Where z=gx,y and dS=-gx,-gy,1dxdy.

Q: The Wronskian 1. Show that the functions e", cos x and sin x are linearly independent. 2. Show that…

A: 1. The functions ex, cos x and sin x are linearly independent.2. The functions 1, sin2x and cos2x…

Q: (i) Consider the multiple regression containing three independent variables: Y = Bo + B1 X1 + B2X2+…

A: Multiple regrassion is used to develop the equations that describes the relationship among various…

Q: Q3: Find the Wronskian for the following solutions. Y, = 1, Y =In

A: Wronskian= 112ln1+x1-xd1dxddx12ln1+x1-x= 112ln1+x1-x01x+11-x=1x+11-x

Q: Suppose X1, X2, and X3 are independent and N(0.1)-distributed. Com- pute the moment generating…

A: Given function Y= X1X2+X1X3+X2X3 We have to calculate moment generating function

Q: 3. For Z = x²secy,prove that Zxy is equal toZyx

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

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Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: 10

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Q: H.W/ using convolution theorem to find L-1

A: We have to find the Laplace inverse by using convolution theorem

Q: nake/s the DE nonlinear y' =1-xy+ y2

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Q: Let f(x) = 7x2(x – 11) + 12. Find the critical points c that correspond to local minima.

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Q: Find the linearization of y = ev7x at x = 16. (Use symbolic notation and fractions where needed.)

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Q: The ACF of the residual u can be used to check the adequacy of the fitted AR(1) model which has the…

A: The given AR(1) model is: yt=2+0.7yt-1+ut The AR model of order 1 is interpreted as the model in…

Q: Expand xy² + 2x – 3y in powers of (x + 2) and (y – 1) upto third degree | terms.

A: Given ,  f(x,y) = xy2 + 2x - 3y  By Taylor's theorem  f(x,y) = f(a,b) + {(x-a)fx(a,b) +…

Q: Exercise 2: Let 0, and 02 be two independent unbiased estimators of 0 such that Var(01) = o? and…

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Q: Show that e, sin x, cos x are linearly independent using Wronskian Method.

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Q: Find the positive integer A such that t²x" +tx' + t²x = λx has a nontrivial solution satisfying x(0)…

A: Hint: Substitute t=ey , t2x''=D(D-1), tx'=D-1in the given equation and calculate to obtain the…

Q: (c) Find the maximum modulus of f (z) = z2 + 4z when |z| < 1.

A: Given fz=z2+4z when z≤1 Note: Maximum modulus principle: If D is a bounded domain and f is…

Q: Let X and Y have the joint p. d. f . sx+y if 0<x, y < 1 elsewher f (x, y) = %3D The covariance…

A: Given X and Y have the joint p.d.f. fx,y=x+y  if  0&lt;x,y&lt;1    0          elsewhere

Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: Use Dirichlet's principle with n = 10 to find a rational approximation of T.

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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: Let {x; t = 1,2, ...} be a covariance stationary process and define y, = Cov(x, x+h) for h = 0.…

A: It is given that {xt: t = 1,2,…} is a covariate stationary process. It implies that, E(xt) and V(xt)…

Q: 2. If the Wronskian of y1 and y2 is e2" (x² + 5) and y1 = e2", find y2. %3D

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Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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Q: 7] The Wronskian of the functions 1, x, and e -2x is (а) е' -2x (2x+1) (b) 4e-2x (c) -e(2x +1) (d)…

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Q: * Lct X; ~ exp (2) · Show that T= EX, is Su fficient pro pesty of T %3D

A: How to find the sufficient statistic 1. Find the likelihood function 2. Apply the Neymann…

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 6. y′=ln|ty|1−t2+y2

A: A hyperbola is an open curve with two branches, which are symmetric and are mirror images of each…