What is the limit as x approaches 0 of x/(sin(5x)) ?

The limit as x approaches 0 of x/(sin(5x)) is 1/5

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limit as x approaches 0 of x/(sin(5x))

x \to 0 lim (\frac{x}{sin ( 5 x )})

\frac{1}{5}

Decimal

0.2

Solution steps

x \to 0 lim (\frac{x}{sin ( 5 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{cos ( 5 x ) \cdot 5})

Plug in the value

x = 0

= \frac{1}{cos ( 5 \cdot 0 ) \cdot 5}

cos (5 \cdot 0) \cdot 5 = 5

= \frac{1}{5}

What is the limit as x approaches 0 of x/(sin(5x)) ?
The limit as x approaches 0 of x/(sin(5x)) is 1/5