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 function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

f(x) = sinx - sin2x in [0,pi]

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))

Separate the intervals of concavity of the following functions (i) f(x)= sin^(-1)x ,(ii) f(x)=x+sinx

Let A={x:-1 le x le 1}=B be a function f: A to B. Then find the nature of each of the following functions. (i) f(x) = |x| " (ii) " f(x)=x|x| (iii) f(x)=x^(3) " (iv) " f(x)="sin"(pi x)/(2)

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4

Discuss the extrema of the following functions (i)f(x)=|x|,(ii)f(x)=e^(-|x|),(iii) f(x)=x^(2//3)

Prove that the function are increasing for the given intervals: f(x)=sinx+tanx-2x ,x in (0,pi/2)

Find the the domain of following functions: (i) f(x)=sqrt(x^(2)-5) (ii) sin(x^(3)-x)

Prove the each of the following function is differentiable at x=0. (i) f(x) = cos|x| (ii) f(x) = x|x| (iii) f(x)=|x^(3)|(iv) f(x) =(x)/(1+|x|)