Limits

Most limit problems on the test can be solved by direct substitution. However, if this results in an indeterminate form like $\frac{0}{0}$, you must try other methods.

Factoring: If you have a rational function, try factoring the numerator and denominator to cancel common terms. For example, $\lim_{x\to2} \frac{(x-2)(x+3)}{(x-2)(x+5)} = \lim_{x\to2} \frac{x+3}{x+5} = \frac{5}{7}$.

L'Hôpital's Rule: For indeterminate forms $\frac{0}{0}$ or $\frac{\infty}{\infty}$, you can take the derivative of the numerator and denominator separately and then evaluate the limit. For example, $\lim_{x\to0} \frac{\sin x}{x} = \lim_{x\to0} \frac{\cos x}{1} = 1$.