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

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

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limit as x approaches+0-of (sin(|x|))/x

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

- 1

Solution steps

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

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= - 1

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