What is the limit as x approaches 0 of (6cos(x)-6)/x ?

The limit as x approaches 0 of (6cos(x)-6)/x is 0

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limit as x approaches 0 of (6cos(x)-6)/x

x \to 0 lim (\frac{6 cos ( x ) - 6}{x})

0

Solution steps

x \to 0 lim (\frac{6 cos ( x ) - 6}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 6 sin ( x )}{1})

= x \to 0 lim (\frac{- 6 sin ( x )}{1})

Plug in the value

x = 0

= \frac{- 6 sin ( 0 )}{1}

Simplify

\frac{- 6 sin ( 0 )}{1} : 0

= 0

x + 3, \frac{( x + 3 )}{2}

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What is the limit as x approaches 0 of (6cos(x)-6)/x ?
The limit as x approaches 0 of (6cos(x)-6)/x is 0