<s>[INST] 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?
 [/INST] Note that 
$$\sqrt{x^2+1}-x=\frac{1}{\sqrt{x^2+1}+x}\rightarrow 0$$ as $x\rightarrow \infty$
Your expression is equal to 
$$\sqrt{(x+1)^2+1}-(x+1)+2 \rightarrow 2$$ as $x\rightarrow \infty$.
</s>