Let F(x, y, z) = x2y3 + y 2 sin(π z) /π + z2ex-1
a) Find the equation of the tangent plane to the graph of the function z = z(x, y) at the point (x, y) = (1, 1), if z satisfies the equation F(x, y, z) = 2 with z(1, 1) = 1.
b) At the point P(1, 1, 1), determine in which of the two directions ~u = h−4, 3, 0i or ~v = h−3, 0, 4i the value of the function F increases at the faster rate.
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