What is the limit as x approaches 0 of (sin^9(x))/x ?

The limit as x approaches 0 of (sin^9(x))/x is 0

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^9(x))/x

x \to 0 lim (\frac{sin ^{9} ( x )}{x})

0

Solution steps

x \to 0 lim (\frac{sin ^{9} ( x )}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{9 sin ^{8} ( x ) cos ( x )}{1})

Plug in the value

x = 0

= \frac{9 sin ^{8} ( 0 ) cos ( 0 )}{1}

Simplify

\frac{9 sin ^{8} ( 0 ) cos ( 0 )}{1} : 0

= 0

What is the limit as x approaches 0 of (sin^9(x))/x ?
The limit as x approaches 0 of (sin^9(x))/x is 0