What is the limit as x approaches 0 of (sin(-2x))/x ?

The limit as x approaches 0 of (sin(-2x))/x is -2

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limit as x approaches 0 of (sin(-2x))/x

x \to 0 lim (\frac{sin ( - 2 x )}{x})

- 2

Solution steps

x \to 0 lim (\frac{sin ( - 2 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- cos ( 2 x ) \cdot 2}{1})

= x \to 0 lim (\frac{- cos ( 2 x ) \cdot 2}{1})

Plug in the value

x = 0

= \frac{- cos ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

\frac{- cos ( 2 \cdot 0 ) \cdot 2}{1} : - 2

= - 2

x \to 0 + lim ((1 + \frac{3}{x})^{2 x})

x \to 2 lim (\frac{x ^{2} - 5}{x - 2})

x \to 0 + lim (x^{π x})

x \to 0 lim ((1 + 3 x)^{\frac{3}{x}})

x \to 4 lim (x^{2} + 5 x - 35)

What is the limit as x approaches 0 of (sin(-2x))/x ?
The limit as x approaches 0 of (sin(-2x))/x is -2