MAT 1235 Calculus II Section 6.8 Indeterminate Forms and L’Hospital Rule
Friday Quiz: 6.7, 6.8
Homework… WebAssign 6.8
Preview You have some experience with this topic from Lab 01 Definition of Indeterminate Forms When and How to apply the L’Hospital’s Rule to find limits
A Common Theme in calculus - Limits Some limits cannot be evaluated by simplifications and substitutions.
A Common Theme in calculus - Limits Some limits cannot be evaluated by simplifications and substitutions. In section 2.4, we use geometric arguments to prove that
A Common Theme in calculus - Limits A lot of applications We have this limit in Calculus 1-3. Used to prove the derivative of sin(x)
Simple Pendulum When the angle is small, the motion can be modeled by
Definition
L’Hospital’s Rule
Remark
Example 1
Step 1: Check that is an indeterminate form Supporting steps should be done on the right hand column.
Example 1 Step 2: Apply the l’Hospital’s rule
Remark on non-standard notation The following non-standard notation is not acceptable in this class.
Remark on non-standard notation The following non-standard notation is not acceptable in this class.
Example 2
Remarks For some problems, you may need to apply the rule more than once. But make sure you check the condition in step 1 every time you apply the rule.
Example 3
Q&A Q: Can I apply the l’Hospital’s rule if the limit is not in quotient form?
Q&A Q: Can I apply the l’Hospital’s rule if the limit is not in quotient form? A: Sometimes, we may rewrite the limit into quotient form and then apply the l’Hospital’s rule.
Example 4
Example 5
Example 6
Geometric Meanings
Geometric Meaning
Reminder: ∞ is not a number