91Ó°ÊÓ

Nonremovable discontinuity Give an example of a function \(g(x)\) that is continuous for all values of \(x\) except \(x=-1,\) where it has a nonremovable discontinuity. Explain how you know that \(g\) is discontinuous there and why the discontinuity is not removable.

The sign-preserving property of continuous functions Let \(f\) be defined on an interval \((a, b)\) and suppose that \(f(c) \neq 0\) at some \(c\) where \(f\) is continuous. Show that there is an interval \((c-\delta, c+\delta)\) about \(c\) where \(f\) has the same sign as \(f(c)\) .