How do you find the slant asymptote of $f (x ) = ( 2x^3 + x^2) / (2x^2 - 3x + 3)$ ?

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Answer 1 · 2016-06-28T04:54:17

$y=x+2$

I must obtain an equation of the type

y=mx+n

First I find m by calculating:

$m=lim_(xrarroo) (2x^3+x^2)/(2x^2-3x+3)*1/x$

$m=lim_(xrarroo) (2x^2+x)/(2x^2-3x+3)$

$m=1$

the I calculate n:

$n=lim_(xrarroo) ((2x^3+x^2)/(2x^2-3x+3)-x)$

$n=lim_(xrarroo) (cancel(2x^3)+x^2cancel(-2x^3)+3x^2-3x)/(2x^2-3x+3)$

$n=lim_(xrarroo) (4x^2-3x)/(2x^2-3x+3)$

$n=2$

so the slant asymptote is

$y=x+2$

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