What is the limit as x approaches 0 of x/(sin(4x)) ?

The limit as x approaches 0 of x/(sin(4x)) is 1/4

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limit as x approaches 0 of x/(sin(4x))

x \to 0 lim (\frac{x}{sin ( 4 x )})

\frac{1}{4}

Decimal

0.25

Solution steps

x \to 0 lim (\frac{x}{sin ( 4 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{cos ( 4 x ) \cdot 4})

Plug in the value

x = 0

= \frac{1}{cos ( 4 \cdot 0 ) \cdot 4}

cos (4 \cdot 0) \cdot 4 = 4

= \frac{1}{4}

What is the limit as x approaches 0 of x/(sin(4x)) ?
The limit as x approaches 0 of x/(sin(4x)) is 1/4