Can anyone evaluate these two math problem?

Question

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


and


lim (e^3x - 1)/(e^x - 1)
x=>0


I got 2
for the first one
and
1/3 for the second

Answer 1

For the second one, you have a lim of a 0/0 case. You can apply L'Hopital's (sp?) theroem and I end up w/ a value of 3 for the resulting limit.

Lim [(e^3x-1)/ (e^x-1)] = Lim {d((e^3x-1)]/dx / [d(e^x-1)/dx]} =

Lim [3e^(3x)/e^x] , as x --> 0, The limit appears to be 3.

Answer 2

This makes my brain hurt!