Using l'Hospital theorem evaluate the limit of (x^2+11x-12)/(x-1), for x->1.

We know that l'Hospital theorem could be applied if the
limit gives an indetermination.

We'll verify if the limit
exists, for x = 1.

We'll substitute x by 1 in the
expression of the function.

lim y = lim
(x^2+11x-12)/(x-1)

lim (x^2+11x-12)/(x-1) = 
(1+11-12)/(1-1) = 0/0

We've get an indetermination
case.

We could solve the problem in 2 ways, at
least.

We'll apply L'Hospital
rule:

lim f(x)/g(x) = lim
f'(x)/g'(x)

f(x) = x^2+11x-12 => f'(x) =
2x+11

g(x) = x-1 => g'(x) =
1

lim (x^2+11x-12)/(x-1) = lim
(2x+11)

lim (x^2+11x-12)/(x-1) = 2*1 +
11

lim (x^2+11x-12)/(x-1) =
13