Thread: Urgent! Multivariable Limit Problem!

Can someone please help me find this limit? I have a test tomorrow.

lim as (x,y) approaches (0,0) of (x+y)/(x-xy+y)

Thanks for your help!

Originally Posted by 1.2.3.pi.4

Can someone please help me find this limit? I have a test tomorrow.

lim as (x,y) approaches (0,0) of (x+y)/(x-xy+y)

Thanks for your help!

Does the limit exist? If so, then it's value is the same regardless of how (0, 0) is approached. eg. Approach along the line y = x ....

However, all paths that I have a value of 1. How can I prove that the lim is in fact 1? Is there any inequality that i can use to solve this limit for the squeeze theorem?

Originally Posted by 1.2.3.pi.4

However, all paths that I have a value of 1. How can I prove that the lim is in fact 1? Is there any inequality that i can use to solve this limit for the squeeze theorem?

You can use polar coordinates to show that the limit exists and is equal to 1 (the limit as r --> 0 is independent of theta).