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If ` underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) theta, b gt 0 and theta in ( - pi, pi]`, then the value of ` theta` is

A

`+- ( pi)/( 4)`

B

` +- ( pi)/( 3)`

C

` +- ( pi)/( 6)`

D

` +- ( pi)/( 2)`

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The correct Answer is:
D
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MOTION-LIMIT-EXERCISE-4
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  7. For each t in R let [t] be the greatest integer less than or equal to ...

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  9. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

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  10. If underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) the...

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  12. Let alpha(a) and beta(a) be the roots of the equation {(a+1)^(1//3)-1}...

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  13. The largest value of non-negative integer a for which underset( x rarr...

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  14. Let m and n be the two positive integers greater than 1 . If underset(...

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  15. Let alpha, beta in R such that lim(x ->0) (x^2sin(betax))/(alphax-sin...

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  16. Let f(x) = ((1 - x(1+ |1-x | )) /(|1-x|)) cos(1/(1-x)) for x!=1

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