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

The limit as x approaches 0 of x/(2x+sin(x)) is 1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

2 + cos (0) = 3

= \frac{1}{3}

What is the limit as x approaches 0 of x/(2x+sin(x)) ?
The limit as x approaches 0 of x/(2x+sin(x)) is 1/3