Find the greatest integer less than `(sqrt(2)+1)^6`

Find all the points of discontinuity of the greatest integer function defined by f(x) = [x] where [x] denotes the greatest integer less than or equal to x.

If f(x)=x-[x], where [x] is the greatest integer less than or equal to x, then f(+1/2) is:

If [x] denotes the greatest integer less than or equal to x, then evaluate underset(ntooo)lim(1)/(n^(2))([1.x]+[2.x]+[3.x]+...+[n.x]).

If [x] is the greatest integer less than or equal to x and (x) be the least integer greater than or equal to x and [x]^(2)+(x)^(2)gt25 then x belongs to

If [x] dnote the greatest integer less than or equal to x then the equation sin x=[1+sin x ]+[1-cos x ][ has no solution in

If f(x)=e^([cotx]) , where [y] represents the greatest integer less than or equal to y then

If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the greatest integer less than or equal to x, then f'"("sqrt(pi//3)")" is equal to

Let f(x)=x-[x], for ever real number x ,w h e r e[x] is the greatest integer less than or equal to xdot Then, evaluate int_(-1)^1f(x)dx .

The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is the greatest integer less than or equal to gamma ), is discontinuous at a. all integers b. all integers except 0 and 1 c. all integers except 0 d. all integers except 1