need help with limit of integer part ??

Question

I need help with that limit of integer part !!

$$\lim\limits_{x\to\infty} x^2E\left(\frac{1}{x}\right)$$

Where $E(x)$ means the integer part of $x$.

Answer 1

For $x>1$, we have

$$0 <\frac {1}{x}<1$$

thus $$(\forall x>1) \;\; E \left(\frac {1}{x}\right)=0$$

and $$x^2E \left(\frac {1}{x}\right)=0$$

The limit is zero