Question

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

Answer 1

`y=x+2`

Explanation:

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`