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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 0

n = 1 \sum \infty \frac{n}{e ^{4 n}}

\int \frac{2 x ^{2} - 5 x + 2}{x ^{3} + x} d x

\frac{d}{d x} (\frac{- 2}{( x - 1 ) ^{3}})

\int (1 - 2 x)^{2021} d x

x \to + 4 + lim (ln (x - 4))

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