How do you find the limit of $((x^2)-x-2)/(x-1)$ as x approaches $1^+$ ?

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Answer 1 · 2016-12-12T20:28:18

See below.

$lim_(xrarr1^+)(x^2-x-2) = -2$

$lim_(xrarr1^+)(x-1) = 0^+$

So,

$lim_(xrarr1^+)(x^2-x-2)/(x-1)$ has form $(-2)/0^+$ .

As $xrarr1^+$ , the quotient is decreasing without bound.

We write:

$lim_(xrarr1^+)(x^2-x-2)/(x-1) = -oo$

How do you find the limit of ((x^2)-x-2)/(x-1)((x^2)-x-2)/(x-1) as x approaches 1^+1^+?