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(Solved): (5 points) Consider the function f(x,y)=(exx)cos(y). Suppose S is the surface z=f(x,y) (a) Find ...

(5 points) Consider the function \( f(x, y)=\left(e^{x}-x\right) \cos (y) \). Suppose \( S \) is the surface \( z=f(x, y) \)
(5 points) Consider the function . Suppose is the surface (a) Find a vector which is perpendicular to the level curve of through the point in the direction in which decreases most rapidly. vector (b) Suppose is a vector in 3-space which is tangent to the surface at the point lying on the surface above . What is ?

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Subtract using long subtraction.

The result of    is   .
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