We have to find` ` lim (x,y)--> (0,0) [sin(x^2+y^2)/(x^2+y^2)]

Let x^2 + y^2 = t

=> `lim_(t-> 0) sin t/t`

Substituting t = 0 gives 0/0 which is indeterminate. Use l'Hopital's rule and substitute sin t and t by their derivatives

=> `lim_(t->0) cos t/1`

substituting t = 0 gives 1.

**The required limit is 1.**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.