If `x = 1 + a + a^2 + --- oo ` and |a| < 1 , then find a

The domain of the function f(x) = sin ^(-1) ((|x| +5)/(x^2 +1)) is ( -oo , -a ] uu [ a,oo ). then a is equal to :

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

The range of (x ^ (2) -2x + 3) / (x ^ (2) -2x-8) AA x in R is (i) (- oo, 0] uu [1, oo) (ii) [ (1) / (2), 2] (iii) (- oo, - (2) / (9)] uu [1, oo) (iv) (oo, -6] uu ([- 2, oo)

If a,x arereal numbers and |a|<1,|x|<1 then 1+(1+a)x+(1+a+a^(2))x^(2)+...oo is equal to

The function f(x) = [ 1/4(3x^2 + 1), -oo< x<= 1; 5-4x, 1 < x< 4; 4-x, 4 <=x < oo is

Mass particles of 1 kg each are placed along x-axus at x=1, 2, 4, 8, .... oo . Then gravitational force o a mass of 3 kg placed at origin is (G= universal gravitation constant) :-