What is the limit as x approaches 0 of ((sin(4x)))/(2x) ?

The limit as x approaches 0 of ((sin(4x)))/(2x) 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 ((sin(4x)))/(2x)

x \to 0 lim (\frac{( sin ( 4 x ) )}{2 x})

2

Solution steps

x \to 0 lim (\frac{sin ( 4 x )}{2 x})

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

= \frac{1}{2} \cdot x \to 0 lim (\frac{sin ( 4 x )}{x})

Apply L'Hopital's Rule

= \frac{1}{2} \cdot x \to 0 lim (\frac{cos ( 4 x ) \cdot 4}{1})

Plug in the value

x = 0

= \frac{1}{2} \cdot \frac{cos ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{1}{2} \cdot \frac{cos ( 4 \cdot 0 ) \cdot 4}{1} : 2

= 2

What is the limit as x approaches 0 of ((sin(4x)))/(2x) ?
The limit as x approaches 0 of ((sin(4x)))/(2x) is 2