Let $f(x)$ be continuous for all $\mathbb R$. $\lim_{x\to\infty}f(x)=L_1$ and $\lim_{x\to-\infty}f(x)=L_2$ Where $L_1,L_2$ belong to $\mathbb R$.
Prove that $f(x)$ is bounded for all $\mathbb R$.
My problem with this conjecture: Isn't $f(x)$=$1/x$ a counterexample? In this case, $L_1,L_2=0$ and the function is not bounded. Did I miss something?
Thanks in advance.