# Limit in Two variables.

1. Oct 8, 2013

### smatik

1. The problem statement, all variables and given/known data

lim (x,y)$\rightarrow$(0,0) f(x,y)=2*x/(x$^{2}$ + x +y$^{2}$)

2. Relevant equations

used different paths like y=k*x ,where k is a constant and y=k*x^2

3. The attempt at a solution
Got an answer 2 but solution says does not exist. Can anybody convince me that why limit does not exist,without using polar form.

I am currently studying in 1st year of college.

2. Oct 8, 2013

### haruspex

The problem with the paths you chose is that there is one direction you are unable to represent with a finite k. What direction do you think that would be?

3. Oct 11, 2013

### smatik

oh got it thanks man. its the y axis!! The limit comes out to be zero if i put x=1. Thanks!