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

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

lim_(x rarr0)(ln(1+x)^(1+x))/(x^(2))-(1)/(x)

lim_(x rarr 0) (1+ax)^(b/x)=

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

If lim_(x rarr0)(cos x+a sin bx)^((1)/(x))=e^(2), then (a,b) is equal to

lim_(x rarr0)[(ln(1+x)^(1+x))/(x^(2))-(1)/(x)]

lim_(x rarr0)[ln(1+sin^(2)x)cot ln^(2)(1+x)]

lim_(x rarr0)(b^(x)-1)/(a^(x)-1)