exam_1 sample solutions - First Preliminary Exam Math 213...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: First Preliminary Exam Math 213 Spring 2008 Name : Solutions This exam has 6 questions on 7 pages, for a total of 50 points. You have 50 minutes to answer all questions. This is closed book, closed notes exam. Use of calculators and other electronic devices is not permitted. Question Points Score 1 12 2 8 3 5 4 10 5 10 6 5 Total: 50 Multiple Choice No partial credit! 1. Multiple Choice. Circle the correct answer for each question. (a) (4 points) Dr. Dorais favorite number is: A. 17 B. 17 C. 17 D. All of the above! Solution: D (but the other three are also correct). (b) (4 points) The limit lim ( x,y ) (0 , 0) sin(17 x 2- 17 y 2 ) cos(17 x 2 + 17 y 2 ) A. Equals 1. B. Equals 0. C. Equals 17. D. None of the above. Solution: B: The function is continuous at (0 , 0). (c) (4 points) The function f ( x,y ) = x 2- y 2 + 17 x- 17 y + 289: A. Has a local maximum at (0 , 0). B. Has a local minimum at (0 , 0). C. Has a saddle point at (0 , 0). D. None of the above. Solution: D: (0 , 0) is not a critical point of f . Page 2 Short Answer Show your work! 2. Derivatives. (a) (4 points) Compute the gradient of f ( x,y,z ) = y 2 e xz at (1 ,- 2 , 2)....
View Full Document

This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).

Page1 / 7

exam_1 sample solutions - First Preliminary Exam Math 213...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online