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Calculus
Common Limits Cheat Sheet
Complete common limits cheat sheet with standard limits, indeterminate forms, L'Hôpital's rule, and limits at infinity. Free PDF download for calculus students.
Important Standard Limits
| Name | Formula | Notes |
|---|---|---|
| Sine Limit | Fundamental trig limit | |
| Cosine Limit | ||
| Cosine Limit 2 | ||
| Euler's Number | ||
| Euler's Number 2 | ||
| Natural Log | ||
| Exponential |
Limits at Infinity
| Name | Formula | Notes |
|---|---|---|
| Polynomial Growth | ||
| Exponential Dominates | e^x grows faster than any polynomial | |
| Polynomial Dominates Log | ||
| Ratio of Polynomials | Compare leading terms |
Indeterminate Forms
| Name | Formula | Notes |
|---|---|---|
| Zero over Zero | Try factoring, rationalization, or L'Hôpital's rule | |
| Infinity over Infinity | Use L'Hôpital's rule | |
| Zero times Infinity | Rewrite as fraction, then use L'Hôpital | |
| Infinity minus Infinity | Combine fractions or factor | |
| Zero to Zero | Take ln, use L'Hôpital, then exponentiate | |
| One to Infinity | Use ln or write as e^{...} | |
| Infinity to Zero | Take ln, use L'Hôpital |
L'Hôpital's Rule
| Name | Formula | Notes |
|---|---|---|
| L'Hôpital's Rule | Only valid for 0/0 or ∞/∞ forms |
One-Sided Limits
| Name | Formula | Notes |
|---|---|---|
| Right Limit | Approaching from the right | |
| Left Limit | Approaching from the left | |
| Limit Exists |
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