I have to prove that $\lim_{x \to \infty} \frac{3+x}{\sqrt{x}}$ doesn't exist. But since I think it does exist I don't know what to do.
The clue was that we had to consider a proof by contradiction. How should I do this?
Thanks in advance!
I have to prove that $\lim_{x \to \infty} \frac{3+x}{\sqrt{x}}$ doesn't exist. But since I think it does exist I don't know what to do.
The clue was that we had to consider a proof by contradiction. How should I do this?
Thanks in advance!
Suppose the limit exists and equals $L\in\mathbb R$. Then $\lim \sqrt{x}=\lim \frac{3+x}{\sqrt{x}}-\lim \frac{3}{\sqrt{x}}=L-0=L$, a contradiction since we know that $\sqrt{x}\to +\infty$.