1. Calculate the limit of f(x) = x/x as x tends to 0.

Question

2. Calculate the limit of
f(x) = (x^2-1)/(x-1) as x tends to 1.

Answer 1

#1: well, f(x) = 1 for every x≠0

similarly for #2,

f(x) = (x+1) for every x≠1

use your favorite online grapher to show that there is just a hole at the point in question. The limit is clear.