#### Answer

Prove that $\lim\limits_{v\to1}p(v)=p(1)$

#### Work Step by Step

*NOTES TO REMEMBER: $f(x)$ is continuous at $a$ if and only if $$\lim\limits_{x\to a}f(x)=f(a)$$
We consider
$\lim\limits_{v\to1}p(v)$
$=\lim\limits_{v\to1}2\sqrt{3v^2+1}$
$=2\sqrt{\lim\limits_{v\to1}(3v^2+1)}$
$=2\sqrt{3\lim\limits_{v\to1}v^2+\lim\limits_{v\to1}1}$
$=2\sqrt{3\times1^2+1}$
$=p(1)$
Therefore, $p(v)$ is continuous at $1$.