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Let `f` be a real valued function defined on the interval `(0,oo)` by `f(x)=In x+int_(0)^(x)sqrt(1+sint)dt`. Then which of the following statement (s) is (are) true?

A

f''(x) exists for all `x in (0, oo)`

B

f'(x) exists for all `x in (0, oo)` and f' is continuous on `(0, oo)` but not differentiable on `(0, oo)`

C

There exists `alpha gt 1` such that `|f'(x)| lt |f (x)|` for all `x in (0, oo)`

D

There exists `beta gt 0` such that `|f(x)| + |f'(x)| le beta` from all `x in (0, oo)`

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The correct Answer is:
B, C
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