Limxtends to infinityx/modulus of x..?

1 Answer
Jim H
Mar 28, 2018

Please see below.

Explanation:

I am interpreting "x tends to infinity" as meaning "x increases without bound".

x/absx = {(1,"if",x > 0),(-1,"if",x < 0):}

Therefore lim_(xrarroo) x/absx = 1

Bonus Answer

As x tends to minus infinity (as x decreases without bound), we have

lim_(xrarr-oo) x/absx = -1

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