calculus - How to solve the limit without graphing $lim_{xtoinfty} frac{x}{sqrt[]{ x^2+1 }}$

What I have tried so far is this

The function $$\lim_{x\to\infty} \frac{x}{\sqrt[]{ x^2+1 }}$$

Seems to be in the Indeterminate Form of $$\frac{\infty}{\infty}$$

Yet the limit when solved using L' Hopital's rule is $$\lim_{x\to\infty} \frac{1}{(\frac{x}{\sqrt[]{x^2+1}})}$$
which equals $$\frac{1}{undefined}$$

but the limit equals 1 not undefined.