The period of `f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x ,` where `n in N ,` is (where `[dot]` represents greatest integer function). `n` (b) 1 (c) `1/n` (d) none of these

lim_(x->0) (lnx^n-[x])/[x], n in N where [x] denotes the greatest integer is

If n in N , the value of int_(0)^(n) [x] dx (where [x] is the greatest integer function) is

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

Evaluate lim{n-> oo) ([1.2x]+[2.3x]+.....+[n.(n+1)x])/(n^3)), where [.] denotes greatest integer function.

The value of int_0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N , is equal to where [.] represents greatest integer function. pi/2(2n-1)-2x pi/2(2n-1)+x pi/2(2n+1)-x (d) pi/2(2n+1)+x

The function f(x)=lim_(nrarroo)cos^(2n)(pix)+[x] is (where, [.] denotes the greatest integer function and n in N )

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

The range of f(x)=[1+sin x]+[2+sin((x)/(2))]+[3+sin((x)/(3))]+...+[n+sin((x)/(n))]AA x in[0,pi) ,where [.] denotes the greatest integer function,is,

Find the value of sum_(n=8)^100[{(-1)^n*n)/2] where [x] greatest integer function