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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Divide by highest denominator power:

\frac{1}{1 + \frac{s i n ( x )}{x}}

= x \to 0 lim (\frac{1}{1 + \frac{s i n ( x )}{x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to 0} ( 1 )}{lim _{x \to 0} ( 1 + \frac{s i n ( x )}{x} )}

x \to 0 lim (1) = 1

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

= \frac{1}{2}

n = 1 \sum \infty (- \frac{1}{3})^{n}

x \to 2 lim (8 + x^{3})

\int \frac{2 y ^{2} - 16}{y ^{2} + 5 y + 6} d y

\frac{d}{d x} ((tan (x))^{c o s (x)})

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