Question

Consider the function f(x,y)=(ex?2x)sin(y). Suppose S is the surfacez=f(x,y).

Consider the function f(x,y)=(ex-2x)sin(y). Suppose S is the surfacez=f(x,y).

(a) Find a vector which is perpendicular to the level curve of through the point (4,6) in the direction in which f decreases most rapidly.
vector =

(b) Suppose v=5i+7j+ais a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4,6). What is a?


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