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

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

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

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

1

Solution steps

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

Divide by highest denominator power:

2 - \frac{sin ( x )}{x}

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to 0 lim (2) = 2

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

= 2 - 1

Simplify

= 1

\int \frac{7 - 2 x}{x ^{\frac{1}{2}}} d x

\frac{d}{d x} (\frac{1}{( a ^{2} + x ^{2} ) ^{\frac{n}{2}}})

\int t^{3} ln (t) d t

\int sin (m x) sin (n x) d x

y = \frac{8 x ^{2} + 2 x + 6}{x}

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