What is the limit as x approaches 0 of (2tan(x))/x ?

The limit as x approaches 0 of (2tan(x))/x is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 0 of (2tan(x))/x

x \to 0 lim (\frac{2 tan ( x )}{x})

2

Solution steps

x \to 0 lim (\frac{2 tan ( x )}{x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 lim (\frac{tan ( x )}{x})

Apply L'Hopital's Rule

= 2 \cdot x \to 0 lim (\frac{sec ^{2} ( x )}{1})

Plug in the value

x = 0

= 2 \cdot \frac{sec ^{2} ( 0 )}{1}

Simplify

2 \cdot \frac{sec ^{2} ( 0 )}{1} : 2

= 2

What is the limit as x approaches 0 of (2tan(x))/x ?
The limit as x approaches 0 of (2tan(x))/x is 2