Page 44 - Calculus for the Clueless, Calc II

Using L'Hopital's rule twice, we find the original limit to be 0.

If you exclude the log examples, all of the preceding could have been done in the first semester. However, the
0
following examples require logs. Those requiring logs are of the form 0 , , and .
Example 9—

0
0 ; by Exmaple 6. So,
.

Example 10—

Since .

Example 11—

Taking derivatives top and bottom, we get

Thus, , so .

Note

Example 12—

k
. No L'Hopital's rule, because 0 = 0 for all positive k.
Note

We use L'Hopital's rule if we have 0/0, , . It's a no-no for .