$\displaystyle \lim_{x \,\to\, 0} \dfrac{\tan{x}}{x}$ formula

Formula

$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\tan{x}}{x}} \,=\, 1$

The limit of quotient of tan of angle by angle as the angle approaches zero is equal to one. It is a standard result in calculus and used as a rule for finding the limit of a function in which tangent is involved.

Introduction

$x$ is a variable and used to represent angle of a right triangle. The tangent function is written as $\tan{x}$ as per trigonometry. The limit of ratio of $\tan{x}$ to $x$ as $x$ tends to zero is often appeared in calculus.

$\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\tan{x}}{x}}$

In fact, the limit of $\tan{(x)}/x$ as $x$ approaches to $0$ is equal to $1$. This standard result in tan function is used as a formula everywhere in the mathematics.