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

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

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limit as x approaches 0 of (sin^8(x))/x

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{8 sin ^{7} ( x ) cos ( x )}{1})

= x \to 0 lim (\frac{8 sin ^{7} ( x ) cos ( x )}{1})

Plug in the value

x = 0

= \frac{8 sin ^{7} ( 0 ) cos ( 0 )}{1}

Simplify

\frac{8 sin ^{7} ( 0 ) cos ( 0 )}{1} : 0

= 0

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