I have to prove the following:

> Let $\phi$ and $\Phi$ denote the standard normal density and distribution functions respectively. Prove that $$\lim_{x\to\infty}{1-\Phi(x)\over \phi(x)/x}=1$$

I am not able to start. $\Phi$ is $\int \phi(x)dx$. How can I calculate the limit **without L'Hopital's rule**?