Unit 10: When plugging in gives 0/0
About this unit
When a limit comes out as 0/0, the ratio of the derivatives of the top and bottom gives the answer, because near the point both behave like their tangent lines.
By the end, you can: Use L'Hôpital's rule to settle 0/0 limits, and see why it works: near the point, top and bottom both look like straight lines through zero.
Modules
5 modulesLearn
- Two things shrinking togetherArticle · 0/0 is a race between two shrinking quantities; near a, f ≈ f′(a)(x − a) and g ≈ g′(a)(x − a), so f/g → f′(a)/g′(a). Check 0/0 first; don't use the quotient rule.Not started
- A limit away from zeroWalkthrough · Apply the rule to ln x/(x − 1) as x → 1: check 0/0, differentiate each part, plug in, and confirm with numbers.Not started
- When once isn't enoughWalkthrough · (1 − cos x)/x² is still 0/0 after one step; apply the rule again to get 1/2, and stop as soon as the form is no longer 0/0.Not started
- The rule on one cardReview · When the rule applies, how to use it, when to repeat, and the two common mistakes.Not started