MATH 114 Midterm: MATH 114 UPenn Exam 2Midterm2

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turquoisegnu128

31 Jan 2019

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Comments: your test will be a mix of multiple choice questions and open answer questions, these problems are taken from old nal examinations. These are the kinds of prob- lems you can expect to see on your test: short solutions are provided at the end. Problem 1: (spring 2009) find the maximum of the function f (x, y, z) = 2x + y z on the surface. 4x2 + 2y2 + z2 = 40. (a) 1 (b) 2 (c) 4 (d) 5 (e) 7 (f ) 10 (g) 13 (h) 25. 2 (c) 2 ( 2 1) (g) 4 (1 1. Problem 3: (spring 2009) the tangent plane to the surface 4x2 + 2y2 + z2 = 10 at (1, 1, 2) intersects the z-axis at a unique point (0, 0, z0). What is z0? (a) 1 (b) 0 (c) 1 (d) 2 (e) 4 (f ) 5 (g) 7 (h) 10.

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How to solve the sort of questions from 100-103? Could anyone write a step by step solution?