MATH 411 Midterm: MATH411 BOYLE-M SPRING2012 0101 MID EXAM 2

• School: University of Maryland
• Department: Mathematics
• Course: MATH 411
• Professor: All

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2. x is a point in rn at which the derivative matrix df (x ) is invertible. Prove that there is a neighborhood u of x such that the function f : u rn is stable: (25 points) de ne the set e to be. E = {(x, y, z) r3 : x > 0, y > 0, z > 0, xyz = 1} . There are more problems on the other side: (25 points) Let e be the set of points (x, y, z) in r3 which are solutions of the following equations: x + y2 + 3z = 0 x3 + z3 + y = 0. De ne a linear function l whose graph is the tangent line or tangent plane (you need to know which) to e near the origin. Show work justifying your answer. (5 points) answer true or false for the following (no justi ca-