# What is the limit of (sin x) / (x^2 + 3x)  as x goes to infinity?

Oct 15, 2015

${\lim}_{x \rightarrow \infty} \frac{\sin \left(x\right)}{{x}^{2} + 3 x} = 0$

#### Explanation:

$\left\mid \sin \left(x\right) \right\mid \le 1 , \forall x$

${\lim}_{x \rightarrow \infty} \left({x}^{2} + 3 x\right) \rightarrow \infty$

The limit of any value less than or equal to a constant
divided by a value that approaches $\infty$ is $0$