What is the limit as x approaches 0+of x/(sin(8x)) ?

The limit as x approaches 0+of x/(sin(8x)) is 1/8

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 x/(sin(8x))

x \to 0 + lim (\frac{x}{sin ( 8 x )})

\frac{1}{8}

Decimal

0.125

Solution steps

x \to 0 + lim (\frac{x}{sin ( 8 x )})

Apply L'Hopital's Rule

= x \to 0 + lim (\frac{1}{cos ( 8 x ) \cdot 8})

Plug in the value

x = 0

= \frac{1}{cos ( 8 \cdot 0 ) \cdot 8}

cos (8 \cdot 0) \cdot 8 = 8

= \frac{1}{8}

What is the limit as x approaches 0+of x/(sin(8x)) ?
The limit as x approaches 0+of x/(sin(8x)) is 1/8