L’Hospital’s Rule Lesson 4.5

Problem There are times when we need to evaluate functions which are rational At a specific point it may evaluate to an indeterminate form

Example of the Problem Consider the following limit: We end up with the indeterminate form Note why this is indeterminate

L’Hospital’s Rule When gives an indeterminate form (and the limit exists) It is possible to find a limit by Note: this only works when the original limit gives an indeterminate form

Example Consider As it stands this could be So we claim

This is not an indeterminate result Example Consider Why is this not a candidate for l’Hospital’s rule? Note also example 7, pg 232 .. the limit must exist This is not an indeterminate result

Example Try When we apply l’Hospital’s rule we get We must apply the rule a second time

Hints Manipulate the expression until you get one of the forms Express the function as a fraction to get

Assignment Lesson 4.5 Page 236 Exercises 1 – 55 EOO