SOLUTIONS TO PRACTICE PROBLEM SET 1
1. 13
To find the limit, we simply plug in 8 for x: (x^2 − 5x − 11) = (8^2 −(5)(8) − 11) = 13.
2.
To find the limit, we simply plug in 5 for x: = =
.
3. 4
If we plug in 3 for x, we get , which is indeterminate. When this happens, we try to factor the
expression in order to get rid of the problem terms. Here we factor the top and get:
= . Now we can cancel the term x − 3 to get (x + 1).
Notice that we are allowed to cancel the terms because x is not 3 but very close to 3. Now we
can plug in 3 for x: (x + 1) = 3 + 1 = 4.
4. + ∞
Here we are finding the limit as x goes to infinity. We divide the top and bottom by the highest
power of x in the expression, which is: x^4 : = . Next,
simplify the top and bottom: . Now, if we take the limit as x goes to infinity,
we get = = ∞.
5.
Here we are finding the limit as x goes to infinity. We divide the top and bottom by the highest
