Limit as (x,y) --> (0,0) for sin(x^2+y^2)/(x^2+y^2)
1 Answer
justaguide | College Teacher | (Level 2) Distinguished Educator
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.