A limit describes what a function approaches as its input gets close to a value, without necessarily reaching it. Direct substitution works when the function is defined at that point. If substitution gives , simplify first: factor and cancel common terms for polynomials, multiply by the conjugate for square roots, or use standard trigonometric limits such as . For limits at infinity of rational functions, divide every term by the highest power of in the denominator. Once the expression is simplified, substitute again to find the limit.
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1| # | Title | Difficulty | Tags | |
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| 136 | A limit worth remembering | Medium |
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| 132620 | Medium | ||
| 132622 | Medium | ||
| 132626 | Give a correct definition of “… as ….” | Medium | |
| 132628 | The limit of … as … is | Medium | |
| 132632 | For … find (a) … (b) … (c) … (d) | Medium | |
| 132634 | If a particular … achieves …, why is it OK to choose… | Medium | |
| 132617 | … (test …) | Medium | |
| 132619 | … (?) | Medium | |
| 132621 | Medium | ||
| 132623 | Medium | ||
| 132624 | (3) | Medium | |
| 132625 | The definition of “… as …” is this: For any … there… | Medium | |
| 132627 | The limit of … as … is ____ | Medium | |
| 132630 | (Calculator) Estimate the limit of … as | Medium | |
| 132631 | For the polynomial … find (a) … (b) … (c) … (d)… | Medium | |
| 132633 | Find the limit as … if it exists: …\frac{3x^2+2x+1}{3+2x+x^2}\qquad \frac{x^4}{x^3+x^2}\qquad \frac{x^2+1000}{x^3-1000}\qquad x\sin\frac{1}{x} | Medium | |
| 132618 | Medium | ||
| 132629 | The limit of … as … does not exist | Medium |