Calculus › Section F · Logarithmic, exponential, and other transcendental functions › Topic F.6
Indeterminate forms and L'Hôpital's rule
Some limits resist every algebraic trick of Section B. L'Hôpital's rule resolves the stubborn 0/0 and ∞/∞ forms by comparing how fast top and bottom move, using derivatives.
In this topic
- The last holdouts
- The rule
- It is not the quotient rule
- Worked example: e^x minus one over x
- Worked example: trig limits, once and twice
- Worked example: powers lose to exponentials
- Worked example: a 0·∞ rewrite
- Power forms: logarithm first
- The cautionary counterexample
- Common mistakes to avoid
- Key takeaways
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Standards: 4