Question

How do you find the slant asymptote of `f(x) = (2x^2 + 3x + 8)/(x + 3)`?

Answer 1

y = 2x-3

Explanation:

Use polynomial long division:

Thus `\frac{2x^2+3x+8}{x+3}=2x-3+\frac{17}{x+3}`
`\lim_{x\to \infty } [2x-3+\frac{17}{x+3}]=2x-3`
`\lim_{x\to -\infty } [2x-3+\frac{17}{x+3}]=2x-3`

Thus the obliques asymptote is `y = 2x-3`