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underset(x to 0)(lim) (1 - cos x)/(x sqr...

`underset(x to 0)(lim) (1 - cos x)/(x sqrt(x^(2))`

A

`(1)/(2) `

B

`-(1)/(2)`

C

0

D

Does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
`lim_(x to 0) (2"sin"^(2)(x)/(2))/(x|x|) `
Now, `lim_( x to 0^(-)) (2"sin"^(2)(n)/(2))/(-x^(2)) rArr lim_(x to 0^(-)) (2"sin"^(2)(x)/(2))/(4xx(x^(2))/(4)) rArr -(1)/(2)`
and `lim_( x to 0^(+)) (2"sin"^(2)(x)/(2))/(+x^(2)) rArr (1)/(2)`
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