`1+(e)/(pi)+(e^(2))/(pi^(2))+(e^(3))/(pi^(3))+...oo`

The value of (lim)_(x rarr1)(2-x)^(tan((pi x)/(2))) is e^(-(2)/(pi)) (b) e^((1)/(pi))(c)e^((2)/(pi))(d)e^(-(1)/(pi))

int_(0)^(pi//2) e^(x^(2))/(e^(x^(2)+ e^((pi/2-x)^(2))))dx=

(pi^(e))/(xe)+(e^(pi))/(x-pi)+(pi^(pi)+e^(e))/(x-pi-e)=0 has

The domain of the function f(x)=(x)/(sqrt(sin(ln x)-cos(ln x))),(n in Z) is (a) (e^(2n pi),e^((3n+(1)/(2))pi)(b))(e^((2n+(1)/(4))pi),e^((2n+(3)/(4))pi))( d) none of these (e^((2n+(1)/(4))pi),e^((2n-(3)/(4))pi))( d) none of these

Consider I_(1)=int_((pi)/(4))^((pi)/(2))(e^(sinx)+1)/(e^(cosx)+1)dx and I_(2)=int_((pi)/(4))^((pi)/(2))(e^(cosx)+1)/(e^(sinx)+1)dx , then

(1) / (2 ^ (2)) tan ((pi) / (2 ^ (2))) + (1) / (2 ^ (3)) tan ((pi) / (2 ^ (3)) ) + .... to oo

The value of lim_(x->1)(2-x)^(tan((pix)/2)) is e^(-2/pi) (b) e^(1/pi) (c) e^(2/pi) (d) e^(-1/pi)

int_(-(pi)/(2))^((pi)/(2))(e^(|sin x|)cos x)/(1+e^(tan x))dx is equal to (a) e+1 (b) 1-(pi)/(2)e(c)e-1(d) none of these

The principal value of sin^(-1)(sin((2 pi)/(3))) is (a)-(2 pi)/(3) (b) (2 pi)/(3) (c) (4 pi)/(3) (d) (5 pi)/(3) (e) none of these

The correct option among the following is (a)pi^(e) e^(pi),(c)pi^(e)=e^(pi),(d) none of these