What is the limit as x approaches 0 of (sin(3x))/(sin(6x)) ?

The limit as x approaches 0 of (sin(3x))/(sin(6x)) is 1/2

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limit as x approaches 0 of (sin(3x))/(sin(6x))

x \to 0 lim (\frac{sin ( 3 x )}{sin ( 6 x )})

\frac{1}{2}

Decimal

0.5

Solution steps

x \to 0 lim (\frac{sin ( 3 x )}{sin ( 6 x )})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (\frac{sin ( 3 x )}{sin ( 6 x )}) = \frac{1}{2}

x \to 0 + lim (\frac{sin ( 3 x )}{sin ( 6 x )}) = \frac{1}{2}

= \frac{1}{2}

What is the limit as x approaches 0 of (sin(3x))/(sin(6x)) ?
The limit as x approaches 0 of (sin(3x))/(sin(6x)) is 1/2