Question

How do you graph `y=tan2pix`?

Answer 1

Using the Socratic facility, I have managed to insert the graph for x of small magnitude. Of course, as `x to (1/4)_ . y to oo` and as`x to (-1/4)_ + , y to -oo`

Explanation:

The period of y=tan kx is `pi/k`. Here, `k=2pi` and the period is 1/2.

So, choose one period, and a good choice is `in (-1/4, 1/4)`.

Using the Socratic facility, I have managed to insert the graph for x

of small magnitude (near 0 ). Of course, as `x to (1/4)_ . y to oo` and as# x

to (-1/4)_ + , y to -oo#

The source for the approximation formula

`y=tan 2pix=2pix+(2pix)^3/3`, nearly, when x is small, is the Maclaurin series

`tan x =x+x^3/3+...`

graph{y= 6.28x+82.7x^3 [-10, 10, -5, 5]}