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})

= 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

\frac{d}{d x} (1 0^{2 x - 1})

\int \frac{x}{x ^{2} x ^{2} - 1} d x

\frac{\partial}{\partial x} (18 y e^{9 x})

\int (x - 9) sin (π x) d x

(\frac{d y}{d x}) + 6 y = e^{- x}

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