How do I prove that lim x->0 (xsin(1/x)) = 0, using the ε, δ definition of a limit?

lim-x-0-xsin1x-0

#1

how do I prove that lim x->0 (xsin(1/x)) = 0, using the ε, δ definition of a limit?

Answer:

It is in the form (sinu)/u, where u= 1/x. Not sure that helps at all. I think the proof is easier with the sqeeze theorem. I honestly don’t even remember how to do an epsilon/delta proof…