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

The limit as x approaches 0 of ((sin^3(2x)))/((sin^3(3x))) is 8/27

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limit as x approaches 0 of ((sin^3(2x)))/((sin^3(3x)))

x \to 0 lim (\frac{( sin ^{3} ( 2 x ) )}{( sin ^{3} ( 3 x ) )})

\frac{8}{27}

Decimal Notation

0.29629 \dots

Solution steps

x \to 0 lim (\frac{sin ^{3} ( 2 x )}{sin ^{3} ( 3 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} ( 2 x )}{sin ^{3} ( 3 x )}) = \frac{8}{27}

x \to 0 + lim (\frac{sin ^{3} ( 2 x )}{sin ^{3} ( 3 x )}) = \frac{8}{27}

= \frac{8}{27}

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What is the limit as x approaches 0 of ((sin^3(2x)))/((sin^3(3x))) ?
The limit as x approaches 0 of ((sin^3(2x)))/((sin^3(3x))) is 8/27