A calculus problem by Abdulrahman El Shafei

The above expression can be rewritten as:

$x \cdot \sqrt{ 1 + \frac{1}{x^2}} = x \cdot \frac{\sqrt{x^2 + 1}}{|x|}$

of which division by zero is not permissible as $x \rightarrow 0$ in this case. Thus the limit doesn't exist.