Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 2 sin(xy), (0, 5) %3D maximum rate of change direction vector

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A: Please note that according to guidelines only first Q is solved.

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A: To Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

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A: I have appended the formula used in the solution part

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Q: he maximum rate of change of f at the given point and the direction in which it occurs. f(x, v) =…

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A: fx,y=y2cos2x∇fx,y=-2y2sin2xi^+2ycos2xj^

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Q: a) Find the derivative of f(x,y) = xe* +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j.

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A: The velocity of the particle is given by, v(t)=sinωtcos8ωt

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Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

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A: Explained below

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Q: Q6:- Show that R = (sin t)i + (cos t)j + v3k has a constant length. And R(t) is orthogonal to its…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

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A: SOLUTION-

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Q: Find the derivative of f(x,y) = xe² +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j .

A: Since you have asked multiple question, we will solve the first question for you. If you want any…