Let `p=lim_(xto0^(+))(1+tan^(2)sqrt(x))^((1)/(2x))`. Then `log_(e)p` is equal to

Answer

B

Explanation

`p=underset(xto0^(+))lim(1+tan^(2)sqrt(x))^((1)/(2x))(1^(oo)" form")`
`=e^(underset(xto0)lim(1+tan^(2)sqrt(x)-1)(1)/(2x))=e^(underset(xto0+)lim((tansqrt(x))^(2))/(2(sqrt(x))^(2)))=e^((1)/(2))`
`:." "log_(e)p=log_(e)^((1)/(2))=(1)/(2)`