find
lim 3x^2 - 12
x --> 2 -----------------
x-2
a. 0
b. limit does not exist
c. 6
d. 12
e. infinity
Replace x by h + 2. The ratio becomes: (3(h + 2)^2 - 12)/(h + 2 - 2), or (3h^2 + 12h)/h → 3h + 12
When x → 2 we want h → 0, which means the ratio tends to 12.
.