Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.2 Algebra Techniques for Finding Limits - 14.2 Assess Your Understanding - Page 884: 53

$1$

$$\lim_{x\to 0}\frac{\tan{x}}{x}\\=\lim_{x\to 0}\dfrac{\frac{\sin{x}}{\cos{x}}}{x}\\=\lim_{x\to 0}(\frac{\sin{x}}{\cos{x}}\frac{1}{x})\\=\lim_{x\to 0}(\frac{\sin{x}}{x}\frac{1}{\cos{x}})\\=\lim_{x\to 0}(1\cdot\frac{1}{\cos{x}})\\=\frac{1}{\cos{0}}\\=\frac{1}{1}=1.$$