Answer
$$1$$
Work Step by Step
In order to simplify the above expression, we will use the following rules.
$(a) \lim\limits_{x \to a} [p(x) \cdot q(x)]=\lim\limits_{x \to a} p(x) \lim\limits_{x \to a} q(x) \\ (b) \lim\limits_{x \to a} k(x)=k(a)$
where $a$ is a constant.
Thus, we have:
$\lim\limits_{x\to 0}\dfrac{\tan{x}}{x}\\=\lim\limits_{x\to 0}\dfrac{\sin x/\cos x}{x}\\=\lim\limits_{x\to 0}(\dfrac{\sin{x}}{x})(\dfrac{1}{\cos{x}})\\=(1) (\lim\limits_{x\to 0}\dfrac{1}{\cos{x}})\\=\dfrac{1}{\cos{0}}\\=\dfrac{1}{1} \\=1$
