Handouts for Section 7.7: Computing Limits with L'Hopital's Rule, Study notes of Calculus

Download Handouts for Section 7.7: Computing Limits with L'Hopital's Rule and more Study notes Calculus in PDF only on Docsity! Handouts for Section 7.7 The goal is to compute limits in the case of the indeterminate forms: 
 
 

 

  1. For the indeterminate forms  and , use L’Hopital’s Rule: Suppose  and  aredifferentiable functions with  near  (except possibly at  ). Suppose that "!"#$&%(' )*  +!"#$&%(' ,*  OR THAT +!"#$&%(' ),* .-  and +!"#$&%(' / 0- 1 Then, "!"#$&%(' )*/  +!"#$&%(' 2,*   if the limit on the right side exists, or is  or 3 . Remarks: 4 Before applying l’Hopital’s rule, always verify that the conditions above are satisfied. 4 L’Hopital’s rule is also valid for one-sided limits. 4 L’Hopital’s rule is also valid at infinity (  5-  ). 2. For the indeterminate forms 6 

 
7 , and 8  , rewrite the given expression so that you can apply l’Hopital’s rule (see the examples covered in class). 1