notes001 (82)

# notes001 (82) - @f=@y , @ 2 f=@x@y , and @ 2 f=@y@x . Do...

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

October 4, 2010 NAME____________________________ 1) By considering di/erent paths of approach, show that lim ( x;y ) ! (0 ; 0) x + y x y does not exist. Solution: First we try approaching (0 ; 0) along the y axis (where x = 0 ). This gives us lim ( x;y ) ! (0 ; 0) with x =0 x + y x y = lim y ! 0 0 + y 0 y = 1 . Now let us try approaching (0 ; 0) along the x axis (where y = 0 ). This gives us lim ( x;y ) ! (0 ; 0) with y =0 x + y x y = lim x ! 0 x + 0 x & 0 = 1 . Since two di/erent results were obtained for di/erent paths of approach, we conclude that lim ( x;y ) ! (0 ; 0) x + y x y does not exist. 2) For the function f ( x; y ) = sin (2 x 3 y ) , ±nd @f=@x ,

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: @f=@y , @ 2 f=@x@y , and @ 2 f=@y@x . Do not just write down an-swers. You must include intermediate steps in your calculations. Solution: @f @x = cos (2 x &amp; 3 y ) (2) = 2 cos (2 x &amp; 3 y ) . @f @y = cos (2 x &amp; 3 y ) ( &amp; 3) = &amp; 3 cos (2 x &amp; 3 y ) . 1 @ 2 f @x@y = @ @x ( &amp; 3 cos (2 x &amp; 3 y )) = &amp; 3 ( &amp; sin (2 x &amp; 3 y )) (2) = 6 sin (2 x &amp; 3 y ) . @ 2 f @y@x = @ @y (2 cos (2 x &amp; 3 y )) = 2 ( &amp; sin (2 x &amp; 3 y )) ( &amp; 3) = 6 sin (2 x &amp; 3 y ) . 2...
View Full Document

## This note was uploaded on 02/05/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

### Page1 / 2

notes001 (82) - @f=@y , @ 2 f=@x@y , and @ 2 f=@y@x . Do...

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

View Full Document
Ask a homework question - tutors are online