Limit $\lim_{x\rightarrow\infty}1-x+\sqrt{2+2x+x^2}$ $$\lim_{x\rightarrow\infty}1-x+\sqrt{2+2x+x^2}=\lim_{x\rightarrow\infty}1-x+x\sqrt{\frac{2}{x^2}+\frac 2x+1}=\lim_{x\rightarrow\infty}1=1\neq2$$ as Wolfram Alpha state. Where I miss something?

You should note that you get
$$\sqrt{x^2 + 2x + 2} = \sqrt{(x+1)^2 + 1} \approx (x+1)$$
as you are squaring i.e. $(x+1)^2$ is not approximately equal to $x^2$  since $(x+1)^2 - x^2  \approx 2x$ you can only ignore the constant.
