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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 sin ^{2} ( x ) cos ( x )}{1})

= x \to 0 lim (\frac{3 sin ^{2} ( x ) cos ( x )}{1})

Plug in the value

x = 0

= \frac{3 sin ^{2} ( 0 ) cos ( 0 )}{1}

Simplify

\frac{3 sin ^{2} ( 0 ) cos ( 0 )}{1} : 0

= 0

\frac{d}{d x} (\frac{x - 2}{3 x ^{2} e ^{x}})

f (x) = x^{3} - 4 x^{2} + 4 x, [0, 3]

\frac{3 x}{x ^{2} + 3}

y^{^{'}} = \frac{x}{3 y}

\int \frac{6}{1 - cos ( 3 x )} d x

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