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})

= 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

\int_{0}^{2} π (\frac{1}{x + 4})^{2} d x

\frac{x ^{2}}{y ^{2} - 5} \frac{d y}{d x} = \frac{1}{2 y}

f (x) = ln (81 sin^{2} (x))

\frac{d}{d x} (\frac{2 x + 1}{3 x - 2})

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

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