What is the limit as x approaches 0-of x/(sin(3x)) ?

The limit as x approaches 0-of x/(sin(3x)) is 1/3

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limit as x approaches 0-of x/(sin(3x))

x \to 0 - lim (\frac{x}{sin ( 3 x )})

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

x \to 0 - lim (\frac{x}{sin ( 3 x )})

Apply L'Hopital's Rule

: x \to 0 - lim (\frac{1}{cos ( 3 x ) \cdot 3})

= x \to 0 - lim (\frac{1}{cos ( 3 x ) \cdot 3})

Plug in the value

x = 0

= \frac{1}{cos ( 3 \cdot 0 ) \cdot 3}

cos (3 \cdot 0) \cdot 3 = 3

= \frac{1}{3}

\int_{- 4}^{4} x 16 - x^{2} d x

g (x) = \frac{1}{2 x}, at x = 9

x^{\frac{1}{2}}, x - 2, [0, 4]

7 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = 6

7 tan (x)

What is the limit as x approaches 0-of x/(sin(3x)) ?
The limit as x approaches 0-of x/(sin(3x)) is 1/3