Evaluate the limit of the function [(3+h)^2-9]/h, if h approaches to 0.

If we'll let h=o, we'll get f(0)
undefined.

Since h is cancelling the numerator, that means
that h is the root of the numerator.

We'll expand the
square from numerator and we'll get:

(3+h)^2 = 9 + 6h +
h^2

We'll subtract 9 both
sides:

(3+h)^2 - 9 = 6h +
h^2

We'll re-write the limit of the
function:

lim (6h + h^2)/h = lim
h(6+h)/h

lim h(6+h)/h = lim (6+h) = 6 + 0 =
6

The limit of the function, if h approaches
to 0, is lim [(3+h)^2-9]/h = 6.