Journal A few to practice Don’t forget FRF!!!!!

Limit Review and L’Hopital’s Rule Calculus BC Unit 3 Day 4 Limit Review and L’Hopital’s Rule

Practice: Find the following Limits

Journal A few to practice Don’t forget FRF!!!!!

Limit Remember: A tells us what a function’s y-values are doing as we APPROACH an x-value.

Types of determinate limits from plug in Value: Infinity

Types of determinate limits from plug in 3. Zero

Summary of Limit Forms Determinate

What to do for this case? Direct substitution leads to : An INDETERMINATE form

Indeterminate Form Maybe it’s zero Maybe it’s infinity or undefined Maybe it’s some other number We don’t know…yet

L’Hopital’s Rule If f(a)=g(a)=0 AND and f’(a) and g’(a) exist then . . . .

Back to our problem . . . .

Back in AB Calculus . . . . Graphically we could tell that Today we can show this analytically using L’Hopital’s Rule. FIRST check to see that L’H can be applied!!

You Try . . . .

L’Hopital’s Rule Also applies to Another indeterminate form

Remember when using L’Hopital’s Rule: Always check for an indeterminant form! Calculate Indeterminant form?

More Limits to ∞

Indeterminate Forms: L’Hopital Applies. An indeterminate form could be in disguise: Rewrite as a division problem. Khan Academy Khan Academy

Strategy we used: Rewrite multiplication as division An incognito indeterminate form. We need to transform it to be familiar. Now we can use L’H Strategy we used: Rewrite multiplication as division

Other things to remember about Limits If then x=a is a Vertical Asymptote If then y=b is a Horizontal Asymptote