The value of `lim_(xto0) (1-(cosx)sqrt(cos2x))/(x^(2))` is
The value of `lim_(xto0) (1-(cosx)sqrt(cos2x))/(x^(2))` is
A. `(1)/(3)`
B. `(1)/(2)`
C. `(1)/(6)`
D. `(5)/(12)`
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Correct Answer - D
`underset(xto0)lim(1-cosxsqrt(cos2x))/(x^(2))`
`underset(xto0)lim(1-cosxsqrt(cos2x")")(1+cosxsqrt(cos2x)))/(x^(2)"("1+cosxsqrt(cos2x")"))`
`=underset(xto0)lim(1-cos^(2)x(cos2x))/(2x^(2))`
`=underset(xto0)lim(1-cos^(2)x(2cos^(2)-1))/(2x^(2))`
`=underset(xto0)lim((1-cos^(2)x)(1+2cos^(2)x))/(2x^(2))`
`=underset(xto0)lim(sin^(2)x.(1+2cos^(2)x))/(2x^(2))`
`=(3)/(2)`
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