What is the limit as x approaches 0 of (sin(x))/(sin(2x)) ?

The limit as x approaches 0 of (sin(x))/(sin(2x)) is 1/2

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limit as x approaches 0 of (sin(x))/(sin(2x))

x \to 0 lim (\frac{sin ( x )}{sin ( 2 x )})

\frac{1}{2}

Decimal

0.5

Solution steps

x \to 0 lim (\frac{sin ( x )}{sin ( 2 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( x )}{cos ( 2 x ) \cdot 2})

Plug in the value

x = 0

= \frac{cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2}

Simplify

\frac{cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2} : \frac{1}{2}

= \frac{1}{2}

What is the limit as x approaches 0 of (sin(x))/(sin(2x)) ?
The limit as x approaches 0 of (sin(x))/(sin(2x)) is 1/2