CK12 Calculus - Single Variable

Herewe observethat we still havethe indeterminateform. So we applyL’Hospital’s Rule againto find
the limit as follows:

L'Hospital'sRule can be usedrepeatedlyon functionslike this. It is oftenusefulbecausepolynomialfunctions
can be reducedto a constant.
LessonSummary

1. 
   

   We learnedto examineend behaviorof functionson infiniteintervals.

   
   


2. 
   

   We determinedhorizontalasymptotesof rationalfunctions.

   
   


3. 
   

   We examinedindeterminateformsof limitsof rationalfunctions.

   
   


4. 
   

   We appliedL’Hospital’s Rule to find limitsof rationalfunctions.

   
   


5. 
   

   We examinedinfinitelimitsat infinity.
   ReviewQuestions

   
   


6. 
   

   Use your graphingcalculatorto estimate

   
   


7. 
   

   Use your graphingcalculatorto estimate
   In problems#3–10,use L’Hospital’s Rule to computethe limits,if they exist.

   
   


8. 
   


9. 
   


10. 
    


11. 
    


12. 
    


13. 
    


14.