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

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

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

θ \to 0 lim (\frac{cos ( θ ) - 1}{θ})

0

Solution steps

θ \to 0 lim (\frac{cos ( θ ) - 1}{θ})

Apply L'Hopital's Rule

= θ \to 0 lim (\frac{- sin ( θ )}{1})

Plug in the value

θ = 0

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

Simplify

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

= 0

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