Consider the function f(x, y) = xe" and the point P(2,0). (a) Find a unit vector that gives the direction of steepest ascent at P, and (b) Find a vector that points in a direction of no change in the function at P.

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

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A: Topic:- polynomial

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A: answer is in next step.

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A: Let's draw the graph.

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A: answer is in next step. please give a like!!

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A: The objective is to find curl F.

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A: Our Aim is to evaluate the integral given below:-∫cos4 (x)1+cos (x) dx -(i)