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

Answer 1

Luke Alvarez

#|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. ,

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Answer 2

Christopher Agresta

The limit of abs(x-2) / (x-2) as x approaches 2^+ is equal to 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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