→PxV in ľ(R) Problem 21 by theorem4A 4-15 fHoung) Let # tet fel'(R_and jel(R, with I&Pf0oaie XER the function it

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Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

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Q: Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of…

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A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: (a) Show that the moment generating function of X is given by 1 Мx() - 1<t< 1. 1 – t2

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Q: 1. (Section 17.4) Use Green's Theorem to evaluate the line integral sir sin(y) dx + x dy, where C is…

A: Use Green theorem.

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Q: (A) Evaluate fz dz along from z 0 to z-4+i along curve of c given by the line from z-0 to z= 2i and…

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Q: (Section 17.3, 17.5) Consider F(a, y) = (e-" cos(y))i + (e-" sin(y))} (a) Show that F is…

A: Here is the solution of the given problem. Line integral:  Conservative Vector Field:

Q: 5. Find the work done by F eyzi + (xzez + zcos(y)j + (1, 0, 1) +(xyevz + sin(y))k from (1,0,1) to…

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Q: 5 of 9 > Let f(x, y, z) = 5x³ · y³ + z². Find the maximum value M for the directional derivative at…

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Q: Let C be the shortest path that connects a to ni and I = . (sinhz + 1)dz %3D O I-sinh rt+ T(i-1) O…

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Q: Use Laplace transforms to solve the initial value problem. x''+x = 9cos2t,  x(0) = 1, x'(0)=0

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Q: Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of…

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Q: a2u a2u =4 at2 au(x,0) où 0 sxs2 with (0,t) = u(2,t) = 0, = 0, %3D %3D %3D at x if 0<x <1 2-х т u(x,…

A: utt =4 uxx               :  0≤x≤2 u0,t = u2,t =0utx,0 =0   ux,0 =x      : 0≤x≤12-x : 1≤x≤2

Q: Theorem 10 Every solution of Eq. (8) satisfies both of the following asymptotic relations Yn+1 lim n…

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Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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Q: 5. Laplaceovou transformáciou riešte rovnicu y" + 4y' + 3y = 8e', y(0+) = y'(0+) = 0.

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Q: Problem 2 4s+3 (s – 1)°(s²+ 4)

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Q: 1. Find the optium path for f=xy³ from (2,1,2)

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

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Q: min ||y – Hx|3 + A ||x||3 x = (H'H + AI)-1H'y (18) In reference to (18), why is HTH+ AI with A > 0…

A: Given - minx y - Hx22 + λx22 ⇒ x = HTH + λI-1HTy           18 To find - In reference to (18), why is…