Check the nature of the following differentiable functions (i) f(x) =`e^(x)`+sin xc,x in `R^(+)` (ii)f(x)=sinx+tan x-`2x,x in(0,pi//2)`

Check the nature of the following differentiable functions (i) f(x) = e^(x) +sin x ,x in R^(+) (ii) f(x)=sinx+tan x- 2x,x in(0,pi//2)

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

Check the validity of the Rolle's theorem for the following functions: f(x) = e^(-x) sin x , x in [0, pi]

If f is a differentiable function and 2f(sinx) + f(cosx)=x AA x in R then f'(x)=

Prove that the following functions are increasing for the given intervals, (i) y =e^(x) + sinx, x epsilon R^(+) (ii) y=sin x+ tan x- 2x, x epsilon(0, pi/2) (iii) y = x + sin x , x epsilon R .

Integrate the following function w.r.t.x (i)f(x)=sinxcos3x (ii) f(x)=sin^(3)x (iii)f(x)=(sinx)/(sin(x-alpha))

Integrate the following function w.r.t.x (i)f(x)=sinxcos3x (ii) f(x)=sin^(3)x (iii)f(x)=(sinx)/(sin(x-alpha))