If `f(x)=(sin([x]pi))/(x^2+x+1)` , where `[dot]` denotes the greatest integer function, then `fi son eon e` `fi snoton e-on ea n dnon-con s t a n t` `fi sacon s t a n tfu n c t ion` `non eoft h e s e`

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

If f(x)=(sin([x]pi))/(x^(2)+x+1) where [.] denotes the greatest integer function,then (A) fis one-one (B) fis not one-one and not constant (C) fis a constant function (D) none of these

f(x)=lim_(n rarr oo)sin^(2n)(pi x)+[x+(1)/(2)], where [.] denotes the greatest integer function,is

f(x)=sin^(-1)[e^(x)]+sin^(-1)[e^(-x)] where [.] greatest integer function then

The value of int_(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greatest integer function of x) is equal to S

The value of int_(-1)^(1)x^(2)e^([x^(3)])dx , where [t] denotes the greatest integer le t , is :

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a)-1 (b) 1 (c) 0 (d) does not exist

Consider two curves C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y , where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is 8/3s qdotu n i t s (b) (10)/3s qdotu n i t s (11)/3s qdotu n i t s (d) (11)/4s qdotu n i t s

If T is the period of the function f(x)=[8x+7]+|tan2 pi x+cot2 pi x|-8x] (where [.] denotes the greatest integer function),then the value of (1)/(T) is