Question

What are the important points to graph `y=sin (2/x)`?

Answer 1

See explanation.

Explanation:

`y=sin(2/x) in [=1, 1]`

`y = 0, x=2/(kpi), k = 0, +-1, +-2, ...`

`y=1, x = 2/((2k+1/2)pi), k = 0, +-1, +-2, +-3, ...`

`y=-1, x = 2/((2k-1/2)pi), k = 0, +-1, +-2, +-3, ...`

The graph meets the x-axis for the last time on the right side at

`x = 2/pi`, and likewise, the last cut on the left is at `x=-2/pi`.

The second graph reveals the decrease ( damping ) of the period of

the waves to the limit 0, as we approach x = 0.

graph{y-sin(2/x)=0 [-5, 5, -2.5, 2.5]}

graph{y-sin(2/x)=0 [-2.5, 2.5, -1.25, 1.248]}