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

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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 )})

= 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}

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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