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 Notation

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})

= 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}

y = (4 x + 3) (2 x^{2} + 7 x - 1)

\int_{0}^{\frac{1}{7}} x arcsin (7 x) d x

\frac{2 d y}{d x} - 4 x y = 8 x, y (0) = 15

\frac{d}{d x} (ln (\frac{1 + x ^{2}}{1 - x ^{2}}))

\int \frac{1}{t ^{2} - 10 t + 29} d t

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