Question

Lim (sin(pi/x)) as x tends to 0 from both sides​

Answer 1

Hello from MrBillDoesMath!

Answer:

Limit does not exist.

Discussion:

The function 1/x has a vertical asymptote as x approaches 0 so

sin (pi/x) has no limit as x approaches 0. In fact, it oscillates wildly between -1 and 1 as x approaches 0. See attached graph of function

Thank you,

MrB