Functions: Limits

Using the definition of a limit (rather than the limit theorems) prove that

     lim {x -> a+}  f(x)

exists and find the limit in each of the following cases

a) f(x) = x/|x|, a = 0.

b) f(x) = x + |x|, a = -1.

c) f(x) = (x - 1)/(x^2 - 1), a = 1.

In which cases do

  lim  {x -> a-}  f(x)    and lim {x -> a} f(x)

also exist?