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

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

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

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

- 4

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- cos ( 4 x ) \cdot 4}{1})

= x \to 0 lim (\frac{- cos ( 4 x ) \cdot 4}{1})

Plug in the value

x = 0

= \frac{- cos ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{- cos ( 4 \cdot 0 ) \cdot 4}{1} : - 4

= - 4

\int \frac{x ^{6}}{x ^{14} - 9} d x

4 + 3 x

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

x = y^{2} - 2, x = 6 - y^{2}

\frac{d}{d x} (\frac{4 x + x ^{2}}{( 2 + x ) ^{2}})

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