Is $ \lim_{x\to \infty}\frac{x^2}{x+1} $ equal to $\infty$ or to $1$? What is 
$ \lim_{x\to \infty}\frac{x^2}{x+1}$? 
When I look at the function's graph, it shows that it goes to $\infty$, but If I solve it by hand it shows that the $\lim \rightarrow 1$
$ \lim_{x\to \infty}\frac{x^2}{x+1} =$ $ \lim_{x\to \infty}\frac{\frac{x^2}{x^2}}{\frac{x}{x^2}+\frac{1}{x^2}} =$ $\lim_{x\to \infty}\frac{1}{\frac{1}{x}+\frac{1}{x^2}}=$$ \lim_{x\to \infty}\frac{1}{0+0} = \ 1$  
what is wrong here?

Hint: Write $$x\cdot \frac{1}{1+\frac{1}{x}}$$
