The sum of the series `x/(1!)+(2x^2)/(2!)+(3x^3)/(3!)+` is `x e^x` b. `-x e^x` c.`x e^x-x` d. `x e^x+x`

Statement -1: The sum of the series (1)/(1!)+(2)/(2!)+(3)/(3!)+(4)/(4!)+..to infty is e Statement 2: The sum of the seies (1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3)+(4)/(4!)x^(4)..to infty is x e^(x)

x gt0 , then the sum of the series e^(-x)-e^(-2x)+e^(-3x)-... i s

The value of lim_(x->0)((1+2x)/(1+3x))^(1/x^2)e^(1/x) is e^(5/2) b. e^2 c. e^(-2) d. 1

int(e^x)/((1+e^x)(2+e^x))dx

int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C (d) x e^(-x)+C

Let x and a be positive real numbers Statement 1: The sum of theries 1+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+(log_(e)x)^(2)+…to infty is x Statement2: The sum of the series 1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)x))^(2)+(x^(3))/(3!)(log_(e)a)^(3)/(3!)+to infty is a^(x)

The value of 1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty

int (e^x +2x)/(e^x+x^2) dx

The value of the integral int_-a^a (x e^(x^2))/(1+x^2)dx is (A) e^(a^2) (B) 0 (C) e^(-a^2) (D) a

Differentiate the following functions with respect to x (a) x^(4) + 3x^(2) -2x (b) x^(2) cos x (c) (6x +7)^(4) (d) e^(x) x^(5) (e) ((1 + x))/(e^(x))