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

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

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

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

3

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

\frac{1 + 2 cos ( 0 )}{1} : 3

= 3

x \to 3 - lim (x^{2} - 1)

x \to 0 + lim ((csc (x))^{3 x})

x \to \infty lim (\frac{2}{6})

x \to 3 lim (\frac{2 - x}{x - 3})

x \to 64 - lim (x - 56)

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