Consider the function f(x, y) = (ex − x)cos y. Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (2, 4) in the direction in which f decreases most rapidly. (Round your components to two decimal places.) $$4.18i−4.08j

-4.18i+4.08 j

Explanation:

We are given that

We have to find the a vector which is perpendicular to the level curve of f through the point in the direction in which f decreases most rapidly.

Grad f(x,y),

Grad f(x,y) at point (2,4) is given by

Hence, the vector which is perpendicular to the level curve of f through the point in the direction in which f decreases most rapidly=-4.18i+4.08 j

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