Mistake Master
Mistake Master · AP Calculus · Unit 4 · Step-Through Animation
A Rule You Have to Earn the Right to Use
You'll learnto substitute before you differentiate, so the rule is only ever applied to a form that qualifies, and to read the number it returns as a statement about the original quotient.
L’Hospital’s Rule is one line: replace the limit of f/g with the limit of f′/g′. The check in front of it is the whole topic, because on the wrong form the rule still hands back a clean, confident number that is not the limit. Ten short steps; press Next for each one.
substitute → read the form → only 0/0 and ∞/∞ open the gate → then f′/g′
Before you start
What you're looking at
A gate. The bar across the top puts x = 2 into the top and bottom of a fraction, prints the form it gets back, and either opens or stays shut. The panel below plots that fraction.
The question
Is this a limit the rule is allowed to touch, and if the rule returns a number anyway, what is that number about?