Find the flux of F(x, y, z) = yi - xj + 2k across S, where S is the helicoid with vector equation r(u, v) = (u cos v, u sin v, v), 0 ≤ u ≤ 1,0 ≤ y ≤ 8.

Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

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Q: 2. Find the gradient of the following scalar functions: a) T = 8/(x+y+2:²) b) V=3x²y³z c) U =…

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Q: One of the following vector functions is a gradient Select one: O (xy? + 2y?)7+ (2y³ – x²y+ 2x)j O…

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A: The given problem is to determine the maximum and minimum directional derivative of the given…

Q: Let the temperature T in degrees at the point (x,y,z), with distances measured in cm, be T(x,y,z)=3x…

A: Here I am attaching image so that you understand each and every step.

Q: Evaluate 1+ x° + y°dS, where S is the helicoid with vector equation т(и, и) — 0 <u < 3, 0 < v< T

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Q: Calculate the directional derivatives of the function x²y x²+ y? for (x, y) +0 f(x,y) = for (x, y)…

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Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

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Q: Let the temperature / in degrees at the point X,y,z), with distances measured in cm, be T(X,y,z)=5x…

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Q: A particle is acted upon by constant forces 4i+j-3k and 3i+j-k and is displaced from the point…

A: Introduction: When a force is acting upon a particle and there is a displacement, the force works on…

Q: Calculate the directional derivatives of functions Inx f (x,y) = x²+ y? in the direction of the…

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Q: 1- a) c) −2ñi + (2ñ + 1)j b) 2πi + (2π − 1)j - 4пi – (2n + 1)j 2лi + (2π + 1)j 4ñi + (2ñ + 1)j Leave…

A: Given:The given function is .To Find:We have to determine the gradient vector of  at the point…

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Q: Compute the directional derivatives of the following functions along unit vectors at the indicated…

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Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =…

A: rate of change of the function at the given point along the given direction

Q: 2yz - 2yz2 + x at the point p = (1, -1, 1), find the unit vector that indicates the direction in…

A: Introduction:   The gradient of the temperature function at the point is the direction of the…