Zayn C.

asked • 01/02/20

Evaluating Problems

Find limit as x approaches 8 from the left of the quotient of the absolute value of the quantity x minus 8, and the quantity x minus 8 

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Peter K. answered • 01/02/20

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x is approaching 8 from the left, so as we can understand by looking at |7.9 - 8| as an example, the expression inside the absolute value is always NEGATIVE so | (x - 8) | = -(x-8) = 8 - x in our x-neighborhood of concern.


So we are effectively being asked to evaluate lim(x-> 8-)[(8-x)/(x-8)]


= lim(x-> 8-)[-1] = -1

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