The sum of the series `1+1/4.2!1/16.4!+1/64.6!+………to oo` is (A) `(e+1)/(2sqrt(e))` (B) `(e-1)/sqrt(e)` (C) `(e-1)/(2sqrt(e))` (D) `(e+1)/2sqrt(e)`

The sum of the series 1/(2!)-1/(3!)+1/(4!)-... upto infinity is (1) e^(-2) (2) e^(-1) (3) e^(-1//2) (4) e^(1//2)

int(e^xdx)/(sqrt(1-e^(x)))

int(e^(2x))/(sqrt(1-e^(2x)))dx

int(e^(x))/(sqrt(e^(2x)-1))dx=

int(dx)/(sqrt(e^(2x)-1))=

int(dx)/(sqrt(2e^(x)-1))=

sec^(-1)((1+e^(2sqrt(x)))/(2e^(sqrt(x)))) differentiate

A variable point P on the ellipse of eccentricity e is joined to the foci S and S'. The eccentricity of the locus of incentre of the triangle PSS' is (A) sqrt((2e)/(1+e)) (B) sqrt((e)/(1+e)) (C) sqrt((1-e)/(1+e))(D)(e)/(2(1+e))

y=e^(sqrt(x))+e^(-sqrt(x))rArr xy_(2)+(y_(1))/(2)=

Evaluate: (i) int((1+sqrt(x))^(2))/(sqrt(x))dx (ii) int sqrt(1+e^(x))e^(x)dx