Use algebra to evaluate the limit.
.......3(2 + h)^2 - 12
lim -------------------------
h->0.........h
........3(h^2 + 4h + 4) - 12
=lim -------------------------------
h ->0........h
..........3h^2 + 12h + 12 - 12
h ->0...........h
..........3h^2 + 12h
=lim ---------------------
h->0........h
=lim 3h + 12
h->0
= 3(0) + 12
= 12 answer//
(3*(h^2 + 4h + 4) - 12)/h
(3h^2 + 12h + 12 - 12)/h
(3h^2 + 12h)/h
3h + 12
now just plug in
as the answer is 12
12 .
because
3(2+h)^2-12=3{(2+h)^2-4}=3{(2+h)^2-2^2}=3(2+h-2)(2+h+2)=3h(h+4)
therefore
[3(2+h)^2-12]/(h)=3(h+4)
when htend to 0, we have 12
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Verified answer
.......3(2 + h)^2 - 12
lim -------------------------
h->0.........h
........3(h^2 + 4h + 4) - 12
=lim -------------------------------
h ->0........h
..........3h^2 + 12h + 12 - 12
=lim -------------------------------
h ->0...........h
..........3h^2 + 12h
=lim ---------------------
h->0........h
=lim 3h + 12
h->0
= 3(0) + 12
= 12 answer//
(3*(h^2 + 4h + 4) - 12)/h
(3h^2 + 12h + 12 - 12)/h
(3h^2 + 12h)/h
3h + 12
now just plug in
as the answer is 12
12 .
because
3(2+h)^2-12=3{(2+h)^2-4}=3{(2+h)^2-2^2}=3(2+h-2)(2+h+2)=3h(h+4)
therefore
[3(2+h)^2-12]/(h)=3(h+4)
when htend to 0, we have 12