Page 42 - Calculus for the Clueless, Calc II
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Chapter 7—
L'hopital's Rule
There was a little on L'Hopital's rule in the volume before. Let us give a complete discussion since we now
know logs.
L'hopital's Rule
1.
2.
then
The value a is any number or plus or minus infinity, and L could be any number or infinity.
This rule states that, if the original limit is zero over zero or infinity over infinity or can be made into that form,
then by taking the derivative of the top and the derivative of the bottom instead of the quotient rule, we can find
the limit of the original.
Example 1—
No L'Hopital's rule.
Example 2—
which means the limit does not exist. Also no L'Hopital's rule.
Example 3—
Yay! L'Hopital's rule can be used.
so
Example 4—
Also 0/0.
