# What is the limit of #lim_((x,y)->(0,0))x^3/(x^2+y^2)#?

##### 1 Answer

Thus, the original limit does not exist.

#### Explanation:

In order for this limit to exist, the fraction

regardless of the path along which we approach

Consider approaching

since the direct compensation product equal

L'Hôpital's rule

since the direct compensation product also equal

L'Hôpital's rule again

Now, consider approaching,(0,0) along the y-axis This means fixing x=0 and finding the limit

Approaching the origin along these two different paths leads to different limits

Thus, the original limit does not exist.