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

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Answer 1 · 2016-06-30T22:20:44

$= oo$

let's say that this amounts to setting $x = 2 + epsilon qquad color{red}{epsilon > 0}$

so we have

$lim_{x to 2^{+}} 1/(x-2) = lim_{epsilon to 0} 1/(2 + epsilon - 2) = lim_{epsilon to 0} 1/epsilon$

because of the statement in red above, this term is positive and so $1/epsilon to + oo$ as $epsilon to 0$

so

$lim_{x to 2^{+}} 1/(x-2) = oo$

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