Find the limit if it exists If the limit does not exist ente

Find the limit, if it exists. (If the limit does not exist, enter DNE in the answer box.)

Solution

Lim(x --> 0 , y --->0) (xy^8/(x^3 + y^12)

Let x = y

Then, Lim(x --> 0 ) [xx^8/( x^3 +x^12)]

Lim (x ---> 0) x^9/( x^3 + x^12)

=0

Let x = 0 , find limit

Lim(x --> 0 , y --->0) (xy^8/(x^3 + y^12)

= 0

Since limit is same in both cases , so limit is 0