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f(x) approaches c as x approaches x0 means that:
for any e > 0, there will be a d(e) > 0 so that
if |x-x0| < d(e), then |f(x)-c| < e
In other words, for any error e there will be an area around x0 as big as d(e)
where the difference between f(x) and c is less than the error e