MATH 103 Final: MATH 103 UPenn 103Fall 05makeup Final Exam
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Math 115 final exam december 2002: consider the surface z = f (x, y) = 2x2 + y2. Find the tangent plane to the surface at the point (x, y, z) = (1, 1, 3) and nd where this plane intersects the z-azis. A. 3 b. 2 c. 0 d. 3 e. 4 f. 6 g. 8 h. 10. If z = f (x, y) is implicitly de ned by the equation x4 + y2 + z2 = 14 in a. 2. neighborhood of (x, y, z) = (1, 2, 3). Y at this point: 4/3 b. 3/2 c. 0 d. 1 e. 5/2 f. 2 g. 2 h. 5/4, let r(x, y) = px2 + y2. Using di erentials to approximate r(2. 9, 4. 1) one gets. 80: the function f (x, y) = x3 + y2 3x + 2y has exactly one saddle point. The value of f at the saddle point is.
