Limits notes
OpenThe 4 formulas you need for Limits, on one page.
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Maths · printable
Limits: One-Page Formula Sheet
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Last updated: 26 October 2026
Formula sheet
Limits formulas
Limits — formula sheet
Formulas
- lim sin x / x = 1, lim (1 − cos x)/x² = ½
- lim (eˣ − 1)/x = 1, lim ln(1 + x)/x = 1
- lim (1 + x)^(1/x) = e
- lim (aˣ − 1)/x = ln a
Key ideas
- Check the form first: 0/0, ∞/∞, 1^∞
- 1^∞ form: limit = e^(lim (f − 1)g)
- Use standard limits before L'Hôpital
- Expansions (series) solve many limits quickly
Traps to avoid
- Using L'Hôpital when the form is not indeterminate
- Forgetting degrees vs radians
- Sign errors with left and right limits
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FAQs
Frequently asked questions
Where can I get a Limits formula sheet PDF for free?
On this page. Use the print button and choose 'Save as PDF'.
How should I use a formula sheet?
Read it once a day for a week, then cover it and write the formulas from memory. Revise only the ones you missed.