How do you find the x values at which #f(x)=x/(x^2-1)# is not continuous, which of the discontinuities are removable?

1 Answer
Jim H
Nov 26, 2017

See below.

Explanation:

This is a rational function.

Rational functions are continuous on their domains.

The domain of this #f# is all reals except #+-1#.

So #f# is discontinuous at #+-1#.

A discontinuity at #a# is removable if #lim_(xrarra)f(x)# exists. But the limit of #f# fails to exist for both #1# and #-1#. So neither discontinuity is removable.

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