Answer
$\dfrac{3}{2}$
Work Step by Step
We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Using this along with the quotient, sum, and root rules for limits, we have
$\lim\limits_{h \to 0}\dfrac{3}{\sqrt{3h+1}+1}=\dfrac{3}{\sqrt{3(0)+1}+1}=\dfrac{3}{\sqrt{0+1}+1}=\dfrac{3}{\sqrt{1}+1}=\dfrac{3}{1+1}=\dfrac{3}{2}.$
