MATH 100 Midterm: MATH 100 KSU Test 2ws s08

• School: Kansas State University
• Department: Mathematics
• Course: MATH 100
• Professor: All

Document Summary

Mathematical economics exam #2, november 9, 2011: let f (x, y, z) = (x + y)z + y. The point (1, 1, 0) satis es the equation f (x, y, z) = 1. If so, let g be the function with f (g(y, z), y, z) = 1 and nd dg(1, 0). Answer: we attempt to apply the implicit function theorem, but calculating f / x = z, we nd f / x(1, 1, 0) = 0. In fact, if we attempt to solve f (x, y, z) = 1 for x, we obtain x = (1 y yz)/z, which is not de ned at z = 0. So x cannot be written as a c 1 function of (y, z) near (1, 1, 0): suppose f (x1, x2, x3) = arcsin(x1x2x 2. 3 ): is f a homogeneous function on r3.