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

The limit as w approaches 0 of (w^2)/(cos(w)-1) is -2

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

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

- 2

Solution steps

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

Apply L'Hopital's Rule

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

Apply L'Hopital's Rule

= w \to 0 lim (\frac{2}{- cos ( w )})

Plug in the value

w = 0

= \frac{2}{- cos ( 0 )}

Simplify

\frac{2}{- cos ( 0 )} : - 2

= - 2

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