Question

Evaluate the limit, or state that the limit does not exist.(6n^2-2n)/(n^2+8)

Answer 1

Assuming the limit is taken as n approaches infinity, we have

`\displaystyle\lim_(n\to\infty)(6n^2-2n)/(n^2+8)=\lim_(n\to\infty)\frac{6-\frac2n}{1+\frac8{n^2}}=\boxed6`

because the rational terms in the numerator and denominator will vanish.