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2.12 Continuity and limits

2.12 Example

The function $f(x)=1/(x-2)$ Then $f$ satisfies

f(x)\rightarrow\infty\qquad{\hbox{as}}\qquad x\rightarrow 2+;

f(x)\rightarrow-\infty\qquad{\hbox{as}}\qquad x\rightarrow 2-;

f(x)\rightarrow 0\qquad{\hbox{as}}\qquad x\rightarrow\pm\infty.

Here $f(x)$ is not defined at $x=2$ ; but this has no bearing on the limiting behaviour as $x$ approaches $2$ .