Correct Answer - D
`lim_(xto0) (2^(|x|)e^(|x|)-|x|log_(2)2-1)/(xtanx)`
`lim_(xto0) (2^(|x|)-|x|log_(2)(2e)-1)/(x^2((tanx)/x))`
`=lim_(xto0) (1+|x|log_e(2e)+(|x|^2)/(2)(log_e(2e))^2+....-|x|log_e(2e)-1)/(x^2((tanx)/x))`
`=lim_(xto0)((|x|^2)/(2)(log_e(2e))^2+....)/(x^2((tanx)/x))=(1)/(2!)(log_e(2e))^2=(1)/(2)(log_e2+1)^2=(1)/(2)(In 2 +1)^2`