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

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

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

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

0

Solution steps

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

\int_{2}^{5} \frac{1}{x - 2} d x

f (x) = (2 x^{3} + 5 x) (x - 3) (x + 2)

x \to π lim (3 cot (x))

\int \frac{15 e ^{5 r}}{e ^{5 r} + 2} d r

\int x^{2} \cdot ln (3 x) d x

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