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

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

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limit as x approaches 0 of (-cos(x)+1)/x

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

0

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

= \frac{sin ( 0 )}{1}

Simplify

\frac{sin ( 0 )}{1} : 0

= 0

\frac{d}{d x} (\frac{x - 5}{( x - 3 ) ( x - 1 )})

\int sin^{5} (\frac{x}{3}) cos (\frac{x}{3}) d x

\int_{- 3}^{1} (x^{2} + 2 x - 3) d x

d er i v a t i v e f (x) = x^{2} (1 - 3 x)

d er i v a t i v e e^{θ}

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