What is the limit as x approaches 0 of (3cos(x)-3)/x ?

The limit as x approaches 0 of (3cos(x)-3)/x is 0

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limit as x approaches 0 of (3cos(x)-3)/x

x \to 0 lim (\frac{3 cos ( x ) - 3}{x})

0

Solution steps

x \to 0 lim (\frac{3 cos ( x ) - 3}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 3 sin ( x )}{1})

= x \to 0 lim (\frac{- 3 sin ( x )}{1})

Plug in the value

x = 0

= \frac{- 3 sin ( 0 )}{1}

Simplify

\frac{- 3 sin ( 0 )}{1} : 0

= 0

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

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

x \to - 1 lim (∣ 3 x ∣)

x \to 0 lim (x^{2} f (x))

x \to 2 - lim (a x + b)

What is the limit as x approaches 0 of (3cos(x)-3)/x ?
The limit as x approaches 0 of (3cos(x)-3)/x is 0