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

The limit as x approaches 0 of x/(sin(9x)) is 1/9

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

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

\frac{1}{9}

Decimal

0.11111 \dots

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

cos (9 \cdot 0) \cdot 9 = 9

= \frac{1}{9}

What is the limit as x approaches 0 of x/(sin(9x)) ?
The limit as x approaches 0 of x/(sin(9x)) is 1/9