" tho "e^(2x+3)

A : log_(e)3+((log_(e)3)^(2))/(2!)+((log_(e)3)^(3))/(3!)+....=2 R : If x,ainRandagt0" then "a^(x)=1+xlog_(e)a+(x^(2))/(2!)(log_(e)a)^(2)+(x^(3))/(3!)(log_(e)a)^(3)+....

The value of x , for which the matrix A = [ {:(e^(x-2) , e^(7+x) ),(e^(2 + x) , e^(2x + 3)):}] is singular, is

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

If y= e^(3 logx +2x , prove that dy/dx = x^2 (2x +3) e^(2x)

int frac{e^(2x) + e^(-2x)}{e^x} dx =............. A) e^x - frac{1}{3 e^(3x)} + c B) e^x + frac{1}{3 e^(3x)} + c C) e^(-x) + frac{1}{3 e^(3x)} + c D) e^(-x) - frac{1}{3 e^(3x)} + c

y = e ^ (2x) + e ^ (3x)

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

Integrate : int (e^(x) dx)/(1-3e^(x)-3e^(2x))