Match the parametrizations to the surfaces shown in the figures. Answer Bank u cos (v) Ф (и, v) —D| и sin (v) (2V1+u² cos (v) O (u, v) =| 2VI+u? sin (v) 3 cos (u) sin (v) O (u, v) = 2 sin (u) sin (v) cos (v) Ф (и, о) %3D u

Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

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Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places.

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Q: F = 5x45 i + ev6 jl and Clis the quarter of the unit circle in the first quadrant, traced…

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Q: Consider the following. u = (2, 0), v = (5, 7) (a) Find u · v. U'V = (b) Find the angle between u…

A: Given that  The vectors  u=(2,0) and v=(5,7) To find the u.v and angle between the u and v

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Q: Bernoulli's equation: Q: dy don + m Sinzy = nicorty Herce, Plw) = e Noww by dividing both sides by…

A: The differential equation of the form, dydx+P(x)y=Q(x)yn is called as Bernoulli's differential…

Q: Example: Find the torsion of the r= (cos t i + sin t j + tk)

A: We use the formula to find the torsion :-

Q: Convert S ² (3 cos 0 + 4r sin² 0) drde СТ [² S²³ (3x+4y2) dyda into polar coordinates 3r+4r sin 0…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x*j+22²yk. div F= curl F=

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Q: Calculate Li eax 1 + ex -dx for 0 < a < 1 using the rectangular contour -R → R → R+ 2πi → -R+ 2πi…

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Q: Gradient. Directional Derivative Find the directional derivative of f(x, y, z) = 2x2 + 3y2 + z2 at…

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Q: y = C¡e e-2= + Cze³* + C2e%

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Q: 1. Find div F and curl F, where F(x,y,z) = sin(xy) z4i + y tan(z²)j – ze²k

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: 5 25- y² 50-g² –y² Convert (x² + y² + z²)dzdædy into spherical coordinates. ²+y² 5/2 pª cos ødpdød0…

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Q: a) Mark the points on the contours where Iz = 0. b 2.

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Q: Prove that v5 is irrational.

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Q: Z is a complex variable z=x+iy  question attached as photo

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Q: Change from rectangular to spherical coordinates. (a) (0, -√3, 1) (p.0.0) =(√10 (6) (4.4, 4√6)…

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