Chapter 1 - Limits and Their Properties - 1.2 Exercises - Page 58: 74

$\lim_{x \to 0} \dfrac{\tan{(nx)}}{x} = n$

Using a graphing utility: For $n=1$ $\lim_{x \to 0} \dfrac{\tan{x}}{x} = 1$ For $n=2$ $\lim_{x \to 0} \dfrac{\tan{2x}}{x} = 2$ For $n=5$ $\lim_{x \to 0} \dfrac{\tan{5x}}{x} = 5$ We notice that the value of the limit is always equal to $n$ $\lim_{x \to 0} \dfrac{\tan{(nx)}}{x} = n$