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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( x ^{9} ) \cdot 9 x ^{8}}{1})

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

Plug in the value

x = 0

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

Simplify

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

= 0

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\int_{1}^{8} \frac{x ^{2} - 1}{x} d x

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