What is the limit as x approaches 0 of (sin^5(x))/x ?

The limit as x approaches 0 of (sin^5(x))/x is 0

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limit as x approaches 0 of (sin^5(x))/x

x \to 0 lim (\frac{sin ^{5} ( x )}{x})

0

Solution steps

x \to 0 lim (\frac{sin ^{5} ( x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{5 sin ^{4} ( x ) cos ( x )}{1})

= x \to 0 lim (\frac{5 sin ^{4} ( x ) cos ( x )}{1})

Plug in the value

x = 0

= \frac{5 sin ^{4} ( 0 ) cos ( 0 )}{1}

Simplify

\frac{5 sin ^{4} ( 0 ) cos ( 0 )}{1} : 0

= 0

\frac{\partial}{\partial y} (3 x^{2} - 5 y)

y^{^{'}} = \frac{x y ^{2} - 0.5 sin ( 2 x )}{y ( 1 - x ^{2} )}

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} = 0

x \to a lim (9)

\frac{2 s + 1}{s ^{2} + 2 s + 5}

What is the limit as x approaches 0 of (sin^5(x))/x ?
The limit as x approaches 0 of (sin^5(x))/x is 0