Review 2 - MAC 2313 SUMMER 2010 Test 2 Review 1) Find and...

Info iconThis preview shows pages 1–2. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAC 2313 SUMMER 2010 Test 2 Review 1) Find and sketch the domain for the following functions. (a) f ( x,y ) = 1- x 2- p 1- y 2 (b) f ( x,y,z ) = ln(16- 4 x 2- 4 y 2- 4 z 2 ). 2) Describe in words or sketch the graph of the following functions. (a) f ( x,y ) = 10- 4 x- 5 y . (b) f ( x,y ) = 4 x 2 + y 2 + 1. (c) f ( x,y ) = x 2 + 1. 3) Find the limit, if it exists, or show that the limit does not exist. (a) lim ( x,y ) (0 , 0) xy 3 x 2 + y 6 (b) lim ( x,y ) (2 , 1) 4- xy x 2 + 3 y 2 (c) lim ( x,y ) (0 , 0) xy 3- yx 3 x 2 + y 2 4) Discuss the continuity of the functions in question 3 (b) at the point (2 , 1) and the function f ( x,y ) = xy 3- yx 3 x 2 + y 2 if ( x,y ) 6 = (0 , 0) 1 if ( x,y ) = (0 , 0) at the point (0 , 0). 5) Use Polar coordinates ( x = r cos , y = r sin ) to find the limits of the following functions. (a) lim ( x,y ) (0 , 0) sin( x 2 + y 2 ) x 2 + y 2 (b) lim ( x,y ) (0 , 0) ( x 2 + y 2 )ln( x 2 + y 2 ) 6) Find the first order partial derivatives of the following functions.6) Find the first order partial derivatives of the following functions....
View Full Document

Page1 / 2

Review 2 - MAC 2313 SUMMER 2010 Test 2 Review 1) Find and...

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