What is the limit as x approaches 0 of (cos(10x)-1)/(x^2) ?

The limit as x approaches 0 of (cos(10x)-1)/(x^2) is -50

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limit as x approaches 0 of (cos(10x)-1)/(x^2)

x \to 0 lim (\frac{cos ( 10 x ) - 1}{x ^{2}})

- 50

Solution steps

x \to 0 lim (\frac{cos ( 10 x ) - 1}{x ^{2}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 10 sin ( 10 x )}{2 x})

= x \to 0 lim (\frac{- 10 sin ( 10 x )}{2 x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 100 cos ( 10 x )}{2})

= x \to 0 lim (\frac{- 100 cos ( 10 x )}{2})

Plug in the value

x = 0

= \frac{- 100 cos ( 10 \cdot 0 )}{2}

Simplify

\frac{- 100 cos ( 10 \cdot 0 )}{2} : - 50

= - 50

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What is the limit as x approaches 0 of (cos(10x)-1)/(x^2) ?
The limit as x approaches 0 of (cos(10x)-1)/(x^2) is -50