Limits

## Description

The limit of a function $f(x)$ as $x\rightarrow x_0$ is the value of the function as the value of $x$ gets closer to $x_0$. The Sage cell below calculates the

(1)
\begin{align} \lim_{x\to 2} \frac{2x}{x-3}. \end{align}

## Sage Cell

#### Code

limit(2*x/(x-3),x=2))


## Options

#### Option

Sometimes the limit of a function is undefined because when approaching any certain $x_0$ value from above $x_0$ will result in a different value than when approaching $x_0$ from below. The Sage Code below shows

(2)
\begin{align} \lim_{x\to 2^-} \frac{2x}{x-3} \end{align}

and

(3)
\begin{align} \lim_{x\to 2^+} \frac{2x}{x-3}. \end{align}

#### Code

limit(2*x/(x-3),x=3, dir='left')
limit(2*x/(x-3),x=3, dir='right')


Primary Tags:

Secondary Tags: