Solution:
We can use L’Hospital’s rule sincethe limit producesthe once is substituted.Hence
A broaderapplicationof L’Hospital’s rule is when is substitutedinto the derivativesof the numerator
and the denominatorbut both still equalzero.In this case,a seconddifferentiationis necessary.
Example6:
Evaluate
Solution:
As you can see, if we applythe limit at this stagethe limit is still indeterminate.So we applyL’Hospital’s rule
again:
ReviewQuestions
Find the limits.
- If is a nonzeroconstantand