Question

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

Answer 1

`y = 7x`

Explanation:

`f(x)=( 21 x^2 ) / ( 3 x + 7)`

you ask specifically about slants wcih means we consider `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