How do you find the limit of $abs(x-2) / (x-2)$ as x approaches $2^+$ ?

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Answer 1 · 2016-04-01T12:13:26

$|x-2|=x-2$ , for x=2+#. For all x > 2, the ratio is 1,

For $x=2-, |x-2|=-(x-2)$ . So, for all x < 2, the ratio = $-1$ .

The right and left limits, as $xto2$ are $+-1$ .

Overall, the graph of y = $|x-2|/(x-2)$ is
$y = -1$ , for x < 2 and y = 1, for x > 2. ,

How do you find the limit of abs(x-2) / (x-2) abs(x-2) / (x-2) as x approaches 2^+2^+?