How do you find the limit of abs(x-3)/ (x-3) as x approaches 3^-?

1 Answer
Steve M
Dec 10, 2016

lim_(x rarr 3^-) |x-3|/(x-3) = -1

Explanation:

\ \ \ \ \ \ lim_(x rarr 3^-) |x-3|/(x-3) = lim_(x rarr 3^-) -(x-3)/(x-3) (as x<3)
:. lim_(x rarr 3^-) |x-3|/(x-3) = lim_(x rarr 3^-) -1
:. lim_(x rarr 3^-) |x-3|/(x-3) = -1

NB { lim_(x rarr 3^+) |x-3|/(x-3) = 1 }

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