Summary of the Limit Laws

The limit laws allow us to evaluate limits of functions without having to go through step-by-step processes each time.
For polynomials and rational functions, $\underset{x\to a}{\lim}f(x)=f(a)$ .
You can evaluate the limit of a function by factoring and canceling, by multiplying by a conjugate, or by simplifying a complex fraction.
The Squeeze Theorem allows you to find the limit of a function if the function is always greater than one function and less than another function with limits that are known.

Key Equations

Basic Limit Results
$\underset{x\to a}{\lim}x=a$
$\underset{x\to a}{\lim}c=c$
Important Limits
$\underset{\theta \to 0}{\lim} \sin \theta =0$
$\underset{\theta \to 0}{\lim} \cos \theta =1$
$\underset{\theta \to 0}{\lim}\frac{\sin \theta}{\theta}=1$
$\underset{\theta \to 0}{\lim}\frac{1- \cos \theta}{\theta}=0$

infinite limit: A function has an infinite limit at a point $a$ if it either increases or decreases without bound as it approaches $a$

intuitive definition of the limit: If all values of the function $f(x)$ approach the real number $L$ as the values of $x(\ne a)$ approach $a$ , $f(x)$ approaches $L$

one-sided limit: A one-sided limit of a function is a limit taken from either the left or the right

vertical asymptote: A function has a vertical asymptote at $x=a$ if the limit as $x$ approaches $a$ from the right or left is infinite