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')
```

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Date: 13 Nov 2018 18:05

Submitted by: James A Phillips