If $\lim_{x \to \infty} (f(x)-g(x)) = 0$ then $\lim_{x \to \infty} (f^2(x)-g^2(x)) = 0\ $: False? 
If $\lim_{x \to \infty} (f(x)-g(x)) = 0$, then $\lim_{x \to \infty} (f^2(x)-g^2(x)) = 0$

My teacher said that the above is false, but I can't find any example that shows that it's false! Can someone explain to me why it's false and also give an example? 

Another example: Let $f(x)=\sqrt{x+1}, g(x)=\sqrt{x}$.
