Page 111 - Calc for the Clueless
P. 111
This kind of question is shorter in length, but it does take practice. So practice!!!
L'hopital's Rule
Unless I can think of something else before this book gets printed, this is the last topic and one of the nicest.
L'Hopital's rule states that if or
where a can be any finite number, plus infinity, or minus infinity, and if
then
Simply put, if the original limit is indeterminate, simply take the derivative of the top and divide it by the
derivative of the bottom, not the quotient rule. If this gives a limit L (or does not exist), then the original limit is
the same.
Example 27—
Using L'Hopital's rule is unnecessary and wrong!
Example 28—
which does not exist—same comment as in the example.
Example 29—
Hooray! L'Hopital's rule applies. Taking the derivative of the top over the derivative of the bottom, we get
So
Example 30—
