`lim_(x->pi)(2-lambda/x)^(2tan((pipi)/(2lambda)))=1/e`, then `lambda` is equal to -

If tan((2 pi)/(3)-x)=(sin(2(pi)/(3)-sin2x))/(cos(2(pi)/(3)-cos2x)) where 0

lim_(lambda rarr0)(int_(0)^(1)(1+x)^(lambda)dx)^((1)/(lambda)) is equal to

If (x+y)^(2)=2(x^(2)+y^(2)) and (xy+lambda)^(2)=4,lambda>0, then lambda is equal to

If int[1+2tan x(tan x+sec x)]^(1/2)dx=lambda log|(tan((x)/(2)+k))/(cos x)|+C then lambda K is equal to where 0 < x < (pi)/(2)

If f(x)=sum_(lambda=1)^(n)(x-(5)/(lambda))(x-(4)/(lambda+1)) then lim_(n rarr oo)f(0) is equal to

If f(x)=sum_(lambda=1)^(n)(x-(5)/(lambda))(x-(4)/(lambda+1)) then lim_(n rarr oo)f(0) is equal to

lim_(lamda to 0)(int_(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal to

If (x+y)^(2)=2(x^(2)+y^(2)) and (x-y+lambda)^(2)=4,lambda>0 then lambda is equal to

If x=(4 lambda)/(1+lambda^(2)) and y=(2-2 lambda^(2))/(1+lambda^(2)) where lambda is a real parameter and Z=x^(2)+y^(2)-xy then possible values of Z can be

lim_(x rarr1)sec^(-1)((lambda^(2))/(ln x)-(lambda^(2))/(x-1)) exists then lambda belong to