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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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 positive when

x \to 0 +

. Therefore

∣ sin (x) ∣ = sin (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 0 lim (+ (sin (\frac{1}{x})))

θ \to 0 lim (cot (θ) - csc (θ))

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

x \to 0 + lim (\frac{4}{x})

x \to 1 lim (x^{\frac{1}{2 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