3 Integrate f(x,y,z) = x + √√y - z³ over the path from (0,0,0) to (3,9,3) given by C₁: r(t) = ti + t²j, 0≤t≤3 C₂: r(t) = 3i+ 9j + tk, 0≤t≤ 3.

Q: Integrate G(x,y,z) = x over the parabolic cylinder y=x², 0≤x≤√√2, 0szs2.

A: The objective is to integrate Gx,y,z=x  over the parabolic cylinder y=x2, 0≤x≤2 and 0≤z≤2. The…

Q: W(s, t) = F(u(s, t), v(s, t)), where F. u. and v are differentiable. If u (6,-6)= -2, u,(6, −6) = 3,…

A: The objective of the question is to find the partial derivatives W_s(6,-6) and W_t(6, -6) for the…

Q: Let f (x, y) = zy(z²–y") (z²+y²) if (x, y) + (0,0) and f (0,0) = 0. af af (a) If (x, y) # (0, 0),…

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Q: f(x,y) = x² + 3y² + +xy b. f(x,y) = /x² + y² a. %3D

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Q: Find the maxima and minima the function f(x, y, z) = xy²z³ under the condi- tions x + y + z = 6, x >…

A: The given function Let

Q: Find the linearization of the function f(x,y) = V9x² + 16y² at the point (1, 1), and use it to…

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Q: 5. Find the linear appoximation for the funciton f(x, y) = (ro, Yo) = (3,0). x-y xy+1 at the point

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Q: Suppose f(x, y) = xy² + 4. Compute the following values: f(4,-5)= ƒ(−5, 4)= f(0,0)= ƒ(5,-5)= f(t,…

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Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: f(x, y) = √√2x² + 5y² fz(0, 1) =

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Q: Let f (x, y, z) = x + yz and let C be the line segment from P = (0, 0, 0) to (8, 6, 6). (a)…

A: Given function is  and let  be the line segment from .And  for .Here, Now,Hence, .Now, Now,Hence, .

Q: Consider f(x, y) = (2x² + xy + 1, xy, x² + y²) and let c = (1,-1). Find Df(c) by definition.

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Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

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Q: f(x, y) = V 2 2 3x² + 4y²

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Q: For f(x, y, z) = x² - y² + z², find f(2, -1, 4).

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Q: Suppose f(x, y) = xy² + 3. Determine each of the following: f(0, -2)= f(-2,0)= f(0,0)= f(-3,-2)=…

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Q: If f(x,y) = 3e2y cos (x-2), then the linear approximation at (2,0) is %3D (A) 3-3x (B) 3+ 6y (C)…

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Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: Let A(t) = 3ti+2]-4k, y B-21-21-3tk and C(t)=-1+3tj+6k. find Ax (B-C) dt

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Q: I grad(f)•dr where C is graph of y = x² + 3x from (0,0) to (2, 14) and f (x,y) = ev/lx*•1}

A: The function is fx, y=eyx+1. Find: ∫Cgradf·dr…

Q: Find the best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

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Q: 2. Let f(x, y) = 4x³y² + 3x²y³, find: (a) Vj (1,2) (b) f(1,2), where u = 17-17

A: (2)  Given that  f x, y = 4x3y2 + 3x2y3  (a)     ∂f∂x = 4y2∂∂xx3 + 3y3∂∂xx2       ⇒ ∂f∂x = 4y23x2 +…

Q: T: M22 --->M22 defined by T(A) = AB,

A: Given, a matrix B, and defined a map T(A) = AB, where T: M2×2  ---> M2×2. We have to find the…

Q: W(s, t) = F(u(s, t), v(s, t)), where F. u. and v are differentiable. If u (6,-6)= -2, u,(6, −6) = 3,…

A: The objective of the question is to find the partial derivatives of W with respect to s and t,…