Question

Please help me solve the following problem. Show that the limit does not exist by considering the limits (x,y)-->(0,0) along the coordinate axes. Click to see the limit...

Answer 1

\[\lim_{(x,y) \rightarrow (0,0)}\frac{ 3 }{ x ^{2}+y ^{2} }\]

Answer 2

apply L'hospital's rule and substitute 0
you will get limit->infinity so limit doesnt exist

Answer 3

I can't use L'Hopital's rule because the limit is not in an indeterminate form.

Answer 4

or consider it as a circle locus with radius r, as x&y reduces to zero the circle in the denominator reduces to a point. so the upper limit tends to infinity