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

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

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

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

- 5

Solution steps

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

Apply L'Hopital's Rule

= x \to 0 lim (\frac{- cos ( 5 x ) \cdot 5}{1})

Plug in the value

x = 0

= \frac{- cos ( 5 \cdot 0 ) \cdot 5}{1}

Simplify

\frac{- cos ( 5 \cdot 0 ) \cdot 5}{1} : - 5

= - 5

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