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

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

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

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

0

Solution steps

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

Divide by highest denominator power:

\frac{sin ( x )}{x} - 1

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

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

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

x \to 0 lim (1) = 1

= 1 - 1

Simplify

= 0

n = 1 \sum \infty 4 (\frac{3}{4})^{n}

\int 2 x \cdot cos (1 + 3 x^{2}) d x

\int \frac{( 7 x ^{3} - 8 x )}{x} d x

\frac{d}{d x} (\frac{5 x ^{2} + 4}{x + 3})

x \to - 1 lim (\frac{( 1 - x )}{x + 1})

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