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})

= 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 t} (\frac{2 t}{1 + 4 t ^{2} + 9 t ^{4}})

\frac{d}{d y} (sin (x y))

\frac{A}{y ^{6}} + B e^{y}

\int_{- \infty}^{0} 2^{x} d x

a \to 0 lim (\frac{cos ( a )}{a})

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