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`

x>0, then the sum of the series e^(-x)-e^(-2x)+e^(-3x)-... is

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

If x gt 0 then the sum of the series e^(-x) - e^(-2x) + e^(-3x) ......infty is

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

The solution of the differential equation (dy)/(dx) = (3e^(2x) + 3e^(4x) )/( e^(x) + e^(-x) ) is a) y= e^(3x) + C b) y=2e^(2x) + C c) y= e^(x) + C d) y= e^(4x) + C

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)

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 number of solution of the equation e^(2 x) + e^x+e^-(2 x)+ e^(-x)=3(e^(-2 x) + e^x) is

The general solution of the differential equation (dy)/(dx) = e^(y) (e^(x) + e^(-x) + 2x) is a) e^(-y) = e^(x) - e^(-x) + x^(2) + C b) e^(-y) = e^(-x) - e^(x) - x^(2) + C c) e^(-y) = -e^(-x) - e^(x) - x^(2) + C d) e^(y) = e^(-x) + e^(x) + x^(2) + C