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}

(- 1, 2), (- 4, - 1)

y^{^{'}} + 4 y = cos (4 t)

\frac{\partial}{\partial y} (3 x^{2} y^{3})

\frac{1}{1 - x ^{2}}

\int csc (\frac{v - π}{2}) cot (\frac{v - π}{2}) d v

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