Expert: Sherry Wallin - 8/17/2010

Question
Hi, i have a multivariable limit that im quite stumped on its f(x,y) = (y-x)*ln(x^2 + y^2), lim f(x,y) as (x,y) -> (0,0). I understand that it needs to be evaluated to lim ln(x)/(1/x) as x -> 0 so it becomes an indeterminate in the form infinite/infinite and then you use L'Hospitals rule to calculate but im unsure how to start to get to the indeterminate form... any help would be much appreciated

Answer
Jaime~
     To use L'Hopital's Rule in an indeterminant form you need to make it 0/0 as the limit of f(x,y) -> (0,0).

(y-x)/[1/ln(x^2 + y^2)] = (y-x)*ln(x^2 + y^2)


(y-x)/[1/ln(x^2 + y^2)] and now is in the indeterminant form 0/0.
Note: 1/00 is one divided by a very large number which is zero for all intents and purposes.

Math Prof