" vi) "(e^(x))/(1+ce^(x))

(d)/(dx){sin^(-1)(e^(x))} is equal to (a) e^(x)sin^(-1)(e^(x)) (b) (e^(x))/(sqrt(1-e^(2x))) (c) (e^(x))/(1-e^(x)) (d) e^(x)cos^(-1)x]]

int2/((e^x+e^(-x))^2)\ dx (a) ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x))+C (c) (-1)/((e^x+1)^2)+C (d) 1/(e^x-e^(-x))+C

A function f: RvecR is defined as f(x)=(lim)_(nvecoo)(a x^2+b x+c+e^(n x))/(1+c.e^(n x)) is continuous on R then find the values of a,b,c.

A function f: RvecR is defined as f(x)=(lim)_(nvecoo)(a x^2+b x+c+e^(n x))/(1+c.e^(n x)) is continuous on R then find the values of a,b,c.

int(1)/(1+e^(x))dx= (a) log(1+e^(x)) (b) log((1+e^(x))/(e^(x))) (c) log(1+e^(-x)) (d) -log(e^(-x)+1)

If y = (e^(x)-e^(-x))/(e^(x)+e^(-x)) then prove that y = (e^(2x)-1)/(e^(2x)+1) .

if int dx/(e^(x) (e^(x)+1)^(2))=(2e^(x)+1)/(e^(x)(e^(x)+1))+ k log|1+e^(-x)|+c then the value of k is -

int((x^(2)+1))/((x+1)^(2))dx is equal to ((x-1)/(x+1))e^(x)+c(b)e^(x)((x+1)/(x-1))+ce^(x)(x+1)(x-1)+c(d) none of these