Here are other examples for you to try, with answers right beneath them. Give ’em a try, and check your
work.
PROBLEM 1. Find .
Answer: If you plug in 3 for x, you get = 0.
PROBLEM 2. Find .
Answer: The left-hand limit is = −∞
If plugging in the value of x results in the denominator equaling
zero and you cannot factor the quotient anymore, then check
the left- and right-hand limits to find the limit of the expression.The right-hand limit is = ∞
These two limits are not the same. Therefore, the limit does not exist.
PROBLEM 3. Find .
Answer: The left-hand limit is = ∞
The right-hand limit is = ∞
These two limits are the same, so the limit is ∞.
PROBLEM 4. Find .
Answer: If you plug −4 into the top and bottom, you get . You have to factor the top into (x + 2)(x + 4) to