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

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: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: Show that (u - v) × (u + v) = 2(u × v)

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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) =…

A: Please see the attachment

Q: 2. Prove: a. [(x)b~ XE]~ = (x)b XA b. Эх (~p(x) A ~q(x)) = ~[Vx(p(x) V q(x))] 3 Dariva

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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: (4-.1.P)an (4-t,t,) and V(t) = (3, t,

A: The given curves are ut=4-t2, t, t2 , vt=3, t2 , t . Let vt=vs →3, s2 , s . Comparing  the…

Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: af (8,9). Let f(x,y)=x?y*. Find ду

A: We are given: f(x,y)=x2y4 ⇒∂f∂y=x24y3=4x2y3

Q: Find af ?х af ду af дz af af 7 Әх ду ах af = = ду af = af дz f(x, y, z) = 3xy + 3xz - 3yz Find their…

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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: 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: Which of the following functions V(y1, Y2) is a Lyapunov function for the dynamical system y1 =…

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Q: 1. Chapter 14 Review 43: Let g(u, v) = f(u³-v³, v³ - u³). Prove that v209 ,მყ dv +4² 0.

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Q: Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at…

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Q: 16. Where does the smallest value f(r, y) + 3ay + y occur on the rectangle (-2, 2) x (-3, 1]? a) It…

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Q: Let g(x, y) = Vx²y². Find 1. g(1, 2) 2. g(4,1) 3. g(2, у) 4. g(x,2) 5. g(w, z – 1)

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