Consider the function f(x, y) = (e – 5x) 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 (3, 4) in the direction in which f decreases most rapidly. vector = <(e^3-5) cos(4),-(e^3-5(3))sin(4)> (b) Suppose v = 4 + 4j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (3, 4). What is a? a =

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