Key Equations

Key Equations

Slope of a Secant Line	$m_{\text{sec}}=\frac{f\left(x\right)-f\left(a\right)}{x-a}$
Average Velocity over Interval $\left[a,t\right]$	$v_{\text{ave}}=\frac{s\left(t\right)-s\left(a\right)}{t-a}$

Intuitive Definition of the Limit	$\underset{x\to a}{\text{lim}}f\left(x\right)=L$
Two Important Limits	$\underset{x\to a}{\text{lim}}x=a\underset{x\to a}{\text{lim}}c=c$
One-Sided Limits	$\underset{x\to a^{-}}{\text{lim}}f\left(x\right)=L\underset{x\to a^{+}}{\text{lim}}f\left(x\right)=L$
Infinite Limits from the Left	$\underset{x\to a^{-}}{\text{lim}}f\left(x\right)=\text{+}\infty \underset{x\to a^{-}}{\text{lim}}f\left(x\right)=\text{−}\infty$
Infinite Limits from the Right	$\underset{x\to a^{+}}{\text{lim}}f\left(x\right)=\text{+}\infty \underset{x\to a^{+}}{\text{lim}}f\left(x\right)=\text{−}\infty$
Two-Sided Infinite Limits	$\underset{x\to a}{\text{lim}}f\left(x\right)=\text{+}\infty :\underset{x\to a^{-}}{\text{lim}}f\left(x\right)=\text{+}\infty$ and $\underset{x\to a^{+}}{\text{lim}}f\left(x\right)=\text{+}\infty$ $\underset{x\to a}{\text{lim}}f\left(x\right)=\text{−}\infty :\underset{x\to a^{-}}{\text{lim}}f\left(x\right)=\text{−}\infty$ and $\underset{x\to a^{+}}{\text{lim}}f\left(x\right)=\text{−}\infty$

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