1. For each of the following statements, determine if the statement is true or false. If the statement is true, provide justification. If the statement is false, give a counter example. [20 points, 5 each] (a) If g(x) is a differentiable function of r, h(y) is a differentiable function of y such that h(y) #0 for all y, and f(, y) = g(I) then h(y) f=(x, y) + fy(x, y) = g'(r)h(y) - g(x)h'(y) h=(y) (b) If f=(a, b) and f,(a, b) both exist, then f(x, y) is differentiable at (a, b). (c) If a > 0 and f(x, y) is continuous, then (d) The following iterated integral will give the volume of a sphere of radius 1. dedydr 1-12-12