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Answer 1 · 2016-06-21T18:15:39

$1/2$

To do this, factor out the highest degree of $x$ from the numerator and denominator.

$lim_(xrarroo)(x-1)/(2x+1)=lim_(xrarroo)(x(1-1/x))/(x(2+1/x))=lim_(xrarroo)(1-1/x)/(2+1/x)$

In evaluating the limit, note that as $x$ approaches $oo$ , $1/x$ will approach $0$ .

So, when the limit is evaluated, the constants remain, and the $1/x$ goes to $0$ :

$lim_(xrarroo)(1-1/x)/(2+1/x)=(1-0)/(2+0)=1/2$