How do you find the slant asymptote of $f (x) = \frac{21 x^{2}}{3 x + 7}$ $f(x)=( 21 x^2 ) / ( 3 x + 7)$ ?

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Answer 1 · 2016-07-06T18:18:55

$y = 7 x$ $y = 7x$

$f (x) = \frac{21 x^{2}}{3 x + 7}$ $f(x)=( 21 x^2 ) / ( 3 x + 7)$

you ask specifically about slants wcih means we consider $x \to \pm \infty$ $x to pm oo$

$lim_{x to pm oo} ( 21 x^2 ) / ( 3 x + 7)$

$= lim_{x to pm oo} ( 21 x ) / ( 3 + 7/x)$

and $lim_{x to pm oo} ( 3 + 7/x) = 3$

so we can identify $y = 21/3 x = 7x$ as a slant asymptote

How do you find the slant asymptote of f(x)=( 21 x^2 ) / ( 3 x + 7)f(x)=21x23x+7f(x)=( 21 x^2 ) / ( 3 x + 7)?