Find the period (if periodic) of the following function ([.] denotes the greatest integer functions): `f(x)=tanpi/2[x]`

Find the period (if periodic) of the following function ([.] denotes the greatest integer functions): f(x)=x-[x-b],b in R

Find the period (if periodic) of the following function ([.] denotes the greatest integer functions): f(x)=(|sinx+cosx|)/(|sinx|+|cosx|)

Find the period (if periodic) of the following function f(x)=e^(log(sinx))+tan^3x-cos e c(3x-5)

Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

Discuss the continuity of the function ([.] represents the greatest integer function): f(x)=[sin^(-1)x]

Discuss the continuity of the function ([.] represents the greatest integer function): f(x)=[(log)_e x]

Draw the graph of y=[|x|] , where [.] denotes the greatest integer function.

Discuss the continuity of the function ([.] represents the greatest integer function): f(x)=[2/(1+x^2)],xgeq0

Find the period of the following. (i) f(x)=(2^(x))/(2^([x])) , where [.] represents the greatest integer function. (ii) f(x)=e^(sinx) (iii) f(x)=sin^(-1)(sin 3x) (iv) f(x) =sqrt(sinx) (v) f(x)=tan((pi)/(2)[x]), where [.] represents greatest integer function.

Evaluate int_(0)^(3) [x]dx ,where [.] denotes the greatest integer function.