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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= 0

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