-If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V (V-F) = V x (V × F) + V² F.

Q: Find fx, fy, fz. fx = + +2² f(x,y,z) = e¯ (4x²+2y² 12=7 Z

A: f(x,y,z)=e-(4x2+2y2+z2)we know (i)  ∂ ∂x(xn)=nxn-1(ii)  ∂ ∂x(constant)=0

Q: Calculate r' (t) and T(t), where r(t) = (2t - 7,2 – 5t, 3 + 5t). r' (t) = (2 T(t) = -5 5

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (2, 1, −2), u'(2) = (7, 1, 8), and v(t) = (t,…

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Q: Let f(t) = 3t4 - 6t+ 3et. Then f'(t) =

A: To find f'(t)

Q: Find ▼ × (V × F) if F(x, y, z) = 6xyj+xyz k. V × (V × F) =

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Q: Let F(x, y, z) = x3³yz² - 6x²yz + 9xz - 2y³z. Find F Fxyz' 3x²yz² - 12xyz +9z+ x³z² − 6x²z − 6y²z +…

A: This question is based on Partial Derivative.

Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: Let f(x,y) = x² - 3xy-y². Compute f(4,0) and f(4, − 3). - f(4,0) = (Simplify your answer.)

A: If you have any help please let me know in comment box and then I will help you.

Q: u = Vx + 5 (x + 1) then du/dx is Зх — 11 Зх + 11 2 Vx + 5 2 Vx + 5 A 3x + 10 Зх — 10 2 Vx + 5 2 Vx +…

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Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

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Q: Find V x (V x F) If F(z,y.2) 10ryj+5zyzk. V x (V x F)

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

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Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: Find r'(t), r''(t), r'(t) · r''(t)

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let Y = min(X1, X2). Find fY (y).

A: We have given that X1,X2∼U(0,1)Objective :To find the  PDF of Y=min(X1,X2)

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: The function u(x, y) obeys, 8²u Ərəy = -2e

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Q: Q1. Let f(x, y) = x²y + x + y² +3. (a). Find f(x, y). (b). Find dy

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Q: let r (t) = The y component of r' (5)

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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: Find V x (V x F) if F(x, y, z) = 5xyj+ 9xyz k. V × (V × F)

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Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

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Q: Find f '(2), where f(t) = u(t) v(t), ū(2) = (1, 2, -1), u' (2) = (3,0, 4), and v(t) = (t, t², t³).

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Q: If z = f(x, y) and z4 – x² = x²y²z? əz Find: dx az and dz ie

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Q: domain and range of f(x,y)

A: Given: f(x,y)=9-x2+y2 -42 To find: Domain and range.

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.