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

If [x] denotes the greatest integer less than or equal to x , then find the value of the integral int_0^2x^2[x]dxdot

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).

Let [x] denote the greatest integer less than or equal to x . If x = (sqrt(3) +1)^(5) , then [x] is equal to

The greatest integer less than or equal to the number log_2(15)xx log_(1/6)2xx log_3(1/6) is

Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x ), then

If [.] denotes the greatest integer less than or equal to the ral number under consideration, and -1lt=x a. [x] b. [y] c. [z] d. none of these

Evaluate: ("lim")_(ntooo)(n^p sin^2 (n !))/(n+1)

The value of lim_(ntooo) [1/n+2] is

The greatest integer less than or equal to 1/(cos290^0)+1/(sqrt(3)sin250^0) is _____