finalsample - Math 252 Fall 2010 Sample Problems for the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 252 Fall 2010 Sample Problems for the Final Exam 1. Let f ( x, y ) = arctan ³ y x ´ . a) Determine the linear approximation to f based at ¡ 3 , 1 ¢ . b) Make use of the result of part a) in order to approximate f (1 . 8 , 0 . 8) (you need not simplify). (Problem 3, Section 2.5). 2. Let f ( x, y )= p x 2 + y 2 . a) Determine the di f erential of f . b) Make use of the di f erential of f in order to approximate f (12 . 1 , 4 . 9) . (Problem 6, Section 2.5). 3. Let f ( x, y )= e x 2 y 2 . a) Compute the gradient of f. b) Compute the directional derivative of f at (2 , 1) in the direction of the vector v = ( 1 , 3) . (Problem 3, Section 2.7). 4. Let f ( x, y )= x 2 3 xy +5 x 2 y +6 y 2 +8 . Determine the nature of the critical points of f (maximum, minimum, or saddle point). (Problem 5, Section 2.8). 5. Let f ( x, y )=3 x 4 y. Make use of Lagrange multipliers to determine the maximum and minimum values of f on the set D = { ( x, y ): x 2 + y 2 =9 . (Problem 2, Section 2.9).
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/13/2010 for the course MATH 252 taught by Professor Bologna during the Spring '03 term at San Diego State.

Page1 / 4

finalsample - Math 252 Fall 2010 Sample Problems for the...

This preview shows document pages 1 - 2. Sign up to view the full document.

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