- Thread starter
- #1

- Thread starter Cbarker1
- Start date

- Thread starter
- #1

- Jan 26, 2012

- 236

Compute limit at $0$. What do you get?

- Thread starter
- #3

- Jan 26, 2012

- 236

So,I got 2.

$$\lim_{x\to 0} \frac{\tan 2x}{x} = 2$$

Now define the function,

$$ f(x) = \left\{ \begin{array}{ccc}(\tan x)/x & \text{if} & x\not = 0 \\ 2 & \text{if}& x=0 \end{array} \right. $$

This function is continous everywhere because at $0$ we have $\lim_{x\to 0}f(x) = f(0) = 2$.