Question

Lim x-->o sin(x)/abs(x)

Answer 1

For x > 0: Lim x-->0+ sin(x)/abs(x) = sin(x)/x = +1
For x < 0: Lim x-->0- sin(x)/abs(x) = sin(x)/(-x) = -1
The limit does not exist because the right side limit is +1 and the left side limit is -1 and and they are not the same.