Build a table to estimate lim sin(1/x) as x approaches zero. Use multiples of pi.

Question

I built a table, but do not understand why this limit does not exist. Please explain! Thank you!!

Answer 1

for a limit L to exist, you need to be able to show that

lim(h->0) |f(h)-L| -> 0

but, no matter how small an h you pick, you can show that there is a k<h such that sin(1/kπ) can be anywhere from -1 to +1