What is the limit as x approaches 0 of (sin^4(x))/x ?

The limit as x approaches 0 of (sin^4(x))/x is 0

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limit as x approaches 0 of (sin^4(x))/x

x \to 0 lim (\frac{sin ^{4} ( x )}{x})

0

Solution steps

x \to 0 lim (\frac{sin ^{4} ( x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{4 sin ^{3} ( x ) cos ( x )}{1})

= x \to 0 lim (\frac{4 sin ^{3} ( x ) cos ( x )}{1})

Plug in the value

x = 0

= \frac{4 sin ^{3} ( 0 ) cos ( 0 )}{1}

Simplify

\frac{4 sin ^{3} ( 0 ) cos ( 0 )}{1} : 0

= 0

\frac{d}{d x} (2500 - x^{2})

\int_{0}^{1} t^{2} e^{- 2 t} d t

\int \frac{e ^{x}}{( e ^{x} - 6 ) ( e ^{2 x} + 1 )} d x

f (x) = \frac{1 - ln ( x )}{x ^{2}}

f (x) = \frac{x}{x + 17}

What is the limit as x approaches 0 of (sin^4(x))/x ?
The limit as x approaches 0 of (sin^4(x))/x is 0