Use properties of limits and algebraic methods to find the limit, if it exists.

lim

h0

2(x+h)²2x²

h

Notice that whenh= 0, the denominator oflim

h0

2(x+h)²2x²

h

is zero.

Recall that if the numerator is also zero whenh= 0, the limit has the indeterminate form0

0

andhis a common factor of the numerator and denominator.

To determine if the numerator is zero whenh= 0, replacehwith 0 in the numerator of the limit and simplify.

2(x+h)²2x²=2(x+ 0)²2x²

=

Thus,lim

h0

2(x+h)²2x²

h

---Select---

has

does not have

the indeterminate form0

0

ath= 0

andh

---Select---

is

is not

a common factor of the numerator and denominator.