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 need to Taylor expand the square root part as well:
Recall that $\sqrt{1+x} = 1 + \frac{1}{2}x + o(x)$ for $x \to 0$
$\sqrt{2/x^2+2/x+1} = (1+\frac{1}{2}2/x+o(1/x)) = 1+1/x + o(1/x)$ as $x \to \infty$
Now you get:
$1-x+x\sqrt{2/x^2+2/x+1} = 1-x+x[1+1/x + o(1/x)] = 2 + o(1) \to 2$ as $x \to \infty$
