A2 - 5. Find a function f : R 2 R such that f x (0 , 0) and...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 237 Assignment 2 Due: Friday, Sept 26th 1. Determine if f is continuous at (0 , 0) where f ( x, y ) = ± sin( xy ) ln( x 2 + y 2 +1) if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) . 2. Determine where the function f ( x, y ) = p x 2 - y 2 is continuous. Justify your answer. 3. Find the partial derivatives of: a) f ( x, y ) = x 2 + 3 xy 2 - y - 2 . b) g ( x, y, z ) = ze xy sin y - 3 x . 4. Let f ( x, y ) = ± x 3 - y 3 x 2 + y 2 , if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) . . a) Find f x (0 , 0) and f y (0 , 0). b) Determine where f is continuous.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5. Find a function f : R 2 R such that f x (0 , 0) and f y (0 , 0) both exist but f is not continuous at (0 , 0). 6. Find the equation of the tangent plane to z = p x 2 + y 2 at the point (1 , 2 , 5). 7. Use the linear approximation to approximate ln ( 1 . 05 (0 . 9) 2 ) ....
View Full Document

This note was uploaded on 04/18/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.

Ask a homework question - tutors are online