MAT 1235 Calculus II Section 6.8 Indeterminate Forms and L’Hospital Rule

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MAT 1235 Calculus II Section 6.8 Indeterminate Forms and L’Hospital Rule

Friday Quiz: 6.7, 6.8

Homework… WebAssign 6.8 Part 1 (Friday, 20 problems, 57 min.) Part 2 (Monday, 6 problems, 22 min.)

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

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

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