Question

How do you use long division find the oblique asymptote `h(x) = 10x^3/(2x^2 -1)`?

Answer 1

`y=5x`

Explanation:

To find the oblique asymptote of this rational function, simply divide `10x^3` by `2x^2-1`, then take the polynomial part (not including the remainder).

Solution:
`color(white)(xxxxxx)ul((5x)(Polynomial Part))`
`2x^2-1|` `color(white)(x)10x^3`
`color(white)(xxxxx)-10x^3+5x`
`color(white)(xxxxxxxxxxxx)5x(Remai` `nder)`

The polynomial part is 5x, so the equation of the oblique asymptote is `y=5x`.