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})

sin (x)

is negative when

x \to 0 -

. Therefore

∣ sin (x) ∣ = - sin (x)

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (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

x \to 6 + lim (x^{3} - c x)

x \to 0 lim (e \frac{1}{x})

x \to 4 lim ((2 x - 3) (4 x + 5))

x \to \infty lim (14)

x \to 3 lim (2 x^{3} - 6 x^{2})

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