What is the limit as x approaches 0 of (sin^7(x))/x ?

The limit as x approaches 0 of (sin^7(x))/x is 0

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limit as x approaches 0 of (sin^7(x))/x

x \to 0 lim (\frac{sin ^{7} ( x )}{x})

0

Solution steps

x \to 0 lim (\frac{sin ^{7} ( x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{7 sin ^{6} ( x ) cos ( x )}{1})

= x \to 0 lim (\frac{7 sin ^{6} ( x ) cos ( x )}{1})

Plug in the value

x = 0

= \frac{7 sin ^{6} ( 0 ) cos ( 0 )}{1}

Simplify

\frac{7 sin ^{6} ( 0 ) cos ( 0 )}{1} : 0

= 0

y^{^{''}} + 4 y = \frac{4}{cos ( 2 t )}

\int - t e^{- t} d t

\int (8 + x^{3})^{5} (3 x^{2}) d x

f (x) = \frac{1}{5 x ^{2} + 4 x}

\int_{1}^{2} (6 x^{2} - 3 x) d x

What is the limit as x approaches 0 of (sin^7(x))/x ?
The limit as x approaches 0 of (sin^7(x))/x is 0