How do you find $lim sqrt(x+2)/(sqrt(3x+1)$ as $x->oo$ ?

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Answer 1 · 2017-03-02T22:03:09

$= 1/sqrt(3)$

$lim_(x to oo) lim sqrt(x+2)/(sqrt(3x+1)$

$= lim_(x to oo) lim (sqrt(x) (sqrt(1+2/(sqrt x))))/(sqrt x (sqrt(3+1/(sqrt x)))$

$= lim_(x to oo) lim ( (sqrt(1+2/(sqrt x))))/( (sqrt(3+1/(sqrt x)))$

$= 1/sqrt(3)$

How do you find lim sqrt(x+2)/(sqrt(3x+1)lim sqrt(x+2)/(sqrt(3x+1) as x->oox->oo?