What is the limit as x approaches 0 of (sin(6x))/(sin(9x)) ?

The limit as x approaches 0 of (sin(6x))/(sin(9x)) is 2/3

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limit as x approaches 0 of (sin(6x))/(sin(9x))

x \to 0 lim (\frac{sin ( 6 x )}{sin ( 9 x )})

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

x \to 0 lim (\frac{sin ( 6 x )}{sin ( 9 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 ( 6 x )}{sin ( 9 x )}) = \frac{2}{3}

x \to 0 + lim (\frac{sin ( 6 x )}{sin ( 9 x )}) = \frac{2}{3}

= \frac{2}{3}

What is the limit as x approaches 0 of (sin(6x))/(sin(9x)) ?
The limit as x approaches 0 of (sin(6x))/(sin(9x)) is 2/3