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

The limit as x approaches 0 of (sin(x)-2x)/x is -1

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

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

- 1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= - 1

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What is the limit as x approaches 0 of (sin(x)-2x)/x ?
The limit as x approaches 0 of (sin(x)-2x)/x is -1