1. ## limit

Find $\lim_{n\to \infty} \frac{n^5+2\sin n}{e^{-n}+6n^5}.$

2. Originally Posted by peteryellow
Find $\lim_{n\to \infty} \frac{n^5+2\sin n}{e^{-n}+6n^5}.$
the largest that $2\sin(n)$ can ever be is 2.

$e^{-n} \to 0$ really fast as $n \to \infty$

so, in essense you have a fraction on the order of $\frac{n^5 + k}{6n^5}$ , where $-2 \le k \le 2$

the limit is $\frac{1}{6}$