Let `p=(lim)_(xvec0+)(1+tan^2sqrt(x))^(1//2x)`then `logp`is equal to:(1) 2(2) 1(3) `1/2`(4)`1/4`A. 2B. 1C. `1/2`D. `1/4`

Let `p=(lim)_(xvec0+)(1+tan^2sqrt(x))^(1//2x)`then `logp`is equal to:(

1.	Let `p=(lim)_(xvec0+)(1+tan^2sqrt(x))^(1//2x)`then `logp`is equal to:(1) 2(2) 1(3) `1/2`(4)`1/4`A. 2B. 1C. `1/2`D. `1/4`
Answer» Correct Answer - C Given, ` p = underset( x to 0^(+)) lim (1+ tan^(2) sqrtx)^(1/(2x) ) ( 1^( infty) " form") ` ` = e^(underset( x to 0^(+)) lim (tan^(2)sqrtx)/(2x)) = e^(1/2 underset( x to 0^(+)) lim ((tan sqrtx)/(sqrtx))^(2))=e^(1/2) ` ` :. " " log p = log e^(1/2) = 1/2 `