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 Notation

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})

= 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}

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x \to \infty lim (\frac{6 x ^{2} + 2 x}{2 x ^{2} - 2 x + 1})

\int cos^{3} (\frac{x}{2}) d x

\frac{π r ^{2} ( π r ^{2} - 1 )}{4}

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