Answer
(a) Use a graph of:
$$f(x) = \frac{\sqrt{3+x}-\sqrt 3}{x}$$
to estimate the value of $\lim\limits_{x \to 0}f(x)$
(b) Use a table of values of $f(x)$ to estimate the limit
(c) Use the limits laws to find the exact value of the limit
Work Step by Step
$$\lim\limits_{x \to 0}\frac{\sqrt {3+x}-\sqrt 3}{x}=
\lim\limits_{x \to 0}\frac{\sqrt {3+x}-\sqrt 3}{x}*\frac{\sqrt {3+x}+\sqrt 3}{\sqrt {3+x}+\sqrt 3} =
\lim\limits_{x \to 0}\frac{{3+x-3}}{x(\sqrt {3+x}+\sqrt 3)}=
\lim\limits_{x \to 0}\frac{{x}}{x(\sqrt {3+x}+\sqrt 3)} =
\lim\limits_{x \to 0}\frac{{1}}{(\sqrt {3+x}+\sqrt 3)} = \frac{{1}}{(\sqrt {3+0}+\sqrt 3)} = \frac{\sqrt 3}{6}
$$
