Let the set `A=(1,oo)uu(-oo,-2)`, find the complement of A w.r.t. R.

If the sum of the series sum_(n=0)^(oo)r^(n),|r|<1 is s then find the sum of the series sum_(n=0)^(oo)r^(2n)

Let f(x) be a cubic polynomial on R which increases in the interval (-oo,0)uu(1,oo) and decreases in the interval (0,1). If f'(2)=6 and f(2)=2, then the value of tan^(-1)(f(1))+tan^(-1)(f((3)/(2)))+tan^(-1)(f(0)) equals

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b)X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c)X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

Let f:(0,oo)vec R be given by f(x)=int_((1)/(x))^(x)(e^(-(t+(1)/(t)))dt)/(t), then (a)f(x) is monotonically increasing on [1,oo)(b)f(x) is monotonically decreasing on (1,oo)(b)f(x) is an odd function of x on R

Let f(x)=sin x and g(x)=(log)_(e)|x| If the ranges of the composition functions fog and gof are R_(1) and R_(2), respectively then (a)R_(1){u:-1<=u<1},R_(2)={v:-oo v<0}(b)R_(1)={u:-oo

The sum sum_(r=2)^(oo)(1)/(r^(2)-1) is equal to

If the set of values of x satisfying [x]>=1-x^(2) is (-oo,-sqrt(a)]uu[b,oo) (where [.] denotes greatest integer function) then find the value of (a+b)

Let A=[x:x in R,|x| =1] and A uu B=R-D, then the set D is