" If "lim_(x rarr0)[1+x log(1+b^(2))]^((1)/(2))=2b sin^(2)theta,b>0" and "theta in(-pi,pi]," then the value of "theta

If lim_(x rarr 0)[1+x ln(1+b^2)]^(1/x)=2b sin^2 theta, b gt 0 "and" theta in (-pi, pi] . then the value of theta is

If lim_(x rarr 0) [1 + x In (1 + b^(2))]^(1/x) = 2b sin^(2) theta, b gt 0 and theta in (-pi, pi] , then the value of theta is :

lim_(x rarr 0) 2/x log (1+x) =

lim_(x rarr0)x sin((1)/(x^(2)))

lim_(x rarr0)(log(1-(x)/(2)))/(x)

lim_(x rarr0)(log(1+x^(2)))/(sin^(2)x) =

lim_(x rarr0)(log(1+x))/(x)=1

lim_(x rarr0)(sin x)/(log_(e)(1+x)^((1)/(2)))

lim_(x rarr0)(sin log(1-x))/(x)

lim_(x rarr0)(sin x+log(1-x))/(x^(2))