MATH 21A Midterm: MATH 20 Harvard 2004Fall20 Midterm III sol
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Full credit may not be given for an answer alone. You may use the backs of the pages or the extra pages for scratch work. Students who, for whatever reason, submit work not their own will ordi- narily be required to withdraw from the college. 1: (10 points) let and be constants such that 0 < < 1 and < 1. Let u(x, y) be the function u(x, y) = (cid:2) x + (1 )y (cid:3) This is just a test of partial derivatives and some algebra. 1/ 1 (1 ) y 1 uxy = (ux)y = (cid:18) 1. Incidentally, u is known as the constant elasticity of substitution function because is (a simpli ed form of) the elasticity of the marginal rate of substitution (ux/uy) with respect to the intensity of x (x/y). 2: (15 points) let s r3 be the surface of points (x, y, z) such that (cid:2)(x 4)2 + y2(cid:3)(cid:2)(x + 4)2 + y2(cid:3) = z4.
