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

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

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

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

0

Solution steps

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

x \to 1 - lim (- \frac{1}{( x - 1 ) ^{2}})

x \to - \infty lim (\frac{8}{x})

x \to 3 + lim (\frac{x}{9 - x ^{2}})

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

x \to - 6 + lim (x + 6 + x)

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