If $f$ is continuous on $[0,1]$ and $f\big(\large\frac{1}{3}\big)$$=1$ then $\lim\limits_{n\to \infty}f(\large\frac{n}{\sqrt{9n^2+1}}\big)$=

Question

$(a)\;1\qquad(b)\;0\qquad(c)\;1/3\qquad(d)\;None\;of\;these$