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

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x2 2 |x| /(2 + x )

Solution

lim x2 2 |x| /(2 + x )

so here -2 is negative

lim x->-2 2 -(x)/(2+x) = 2 -x/(2+x)

= (4 +x) /(2+x)

now if you plug we get infinite from so

we use Lhosiptal rule

then lim x2 2 |x| /(2 + x ) = 1