Answer
$\lim\limits_{x\to\infty}\sqrt{x^2+1}=\infty$
Work Step by Step
$$\lim\limits_{x\to\infty}\sqrt{x^2+1}$$$$=\sqrt{\lim\limits_{x\to\infty}(x^2)+1}$$
As $x\to\infty$, $x^2\to\infty$. Therefore, $\lim\limits_{x\to\infty}(x^2)=\infty$
Which means, $\sqrt{\lim\limits_{x\to\infty}(x^2)+1}=\sqrt{\infty+1}=\infty$
In conclusion, $\lim\limits_{x\to\infty}\sqrt{x^2+1}=\infty$
