1. Chapter 14 Review 43: Let g(u,v) = f(u³ - v3, v³ - u3). Prove that g д + u2 ди ди 2 = = 0.

Q: 1. Let T = [-2 1 0 5], 5 1 1 0 A = [¦ ¦] ·--[¦ ¦ ). -- [¦ ¦ ¦]. - -[] [16], B = = [1 2] C = D = 0 3…

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Q: 1 2 0 0 2 0 0 2 0 0 plain why span M2(R) 0 4 3 4

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Q: Which of the following is not true for the differential operators A, B, and C? A (A+B) +C = A+ (B+C)…

A: Differential operator

Q: Suppose that f: R² R² is a function such that f (1,2)= the linear approximation. (Use syntax like…

A: We have to estimate f (1.1, 2.01) using the linear approximation.

Q: Find the following. = ( ₁₁ — 1) , V₁ 1, = 2 U = (a) ||u|| (b) (c) ||u + v|| (d) (e) ||v|| (f) — 33 u…

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Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .

Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

Q: The equations xy² + 8xzcos(u) + ye" = 16 and xyz + xev – 9u?v² = 27 are solved for u and v as…

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Q: дz az Use the chain rule to find and Əs Ət əz Əs əz at = = ¹(=), z = tan u = 3s + 5t, v = 5s - 3t

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Q: The Doman off(x) = V4 – Vx is

A: Note: The correct option is not in the option.

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(3, 6) = -7, us (3,- 6) =…

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Q: If F(s) = 1/(S-2), then f(t) is %3D a) e²'u(t) c) u(t-2) d) e"'u(t) -2t b) u(t +2)

A: Given Fs=1s−2 We have to find the ft Use definition of inverse Laplace transform, which is given…

Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

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Q: 3) Consider stress of a body at a particular point is give in the form of Q(x1, x2, X3) = xỉ – x –…

A: Given: Qx1,x2,x3=x12-x32-4x1x2+4x2x3   To find: An orthogonal change of variables that eliminates…

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: of have Σ f(m). nez ory" + HAIF bo turn food (A-LAI) - (A) A

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Q: . Find, from first principles, f(2, -1) for f(x, y) = 2a?y³ + e2y. ,2,,3

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Q: Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4.…

A: Suppose f and g are functions such that

Q: T at = 8²T əx² with [B.C] T₂ (0,t)=0, T₂ (2,t) = 0 and [I.C.] 7(x,0)=f(x)

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Q: A Find the value of J G dL if G = x'a, - xyza, given points P,(1,2,3) and P;(5,0,4) and a path…

A: Given: G=x2ax-xyzaz P1:1,2,3 P2:5,0,4   To find: The value of ∫P1P2G·dL for a path consisting of:…

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and u are differentiable. If u(-6,0) = 6, u,(-6,0) = -2,…

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Q: Find a formula for u(x, t) that solves Ихх сис u(x, 0) = and show that (a) \4(x, t) 51

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Q: du du dx' dy 1) u = 3x²y + xlny² - Inxy 2) u =xe*Y+ ‡ ArcTan , 3) u = +2²-3² I. Find and (whenever…

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Q: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi –…

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Q: af Let f(x, y) = x³y + 8. Compute (1, 2) and -(1, 2). ax ду

A: Given: fx,y=x3y+8