Integer part3

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

Let [x] denote the greatest integer part of a real number x, if M= sum_(n=1)^(40)[(n^(2))/(2)] then M equals

If [x] and (x) are the integral part of x and nearest integer to x then solve (x)[x]=1

If x= (8 + 3 sqrt(7))^(n) , where n is a natural number, power that the integral part of x is an odd integer and also show that x - x^(2) + x[x] = 1 , where [.] denotes the greatest integer function .

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

Write four consecutive odd integers preceding 3.

Show that the following integers are cubes of negative integers. Also find the integer whose cube is the given integer. -5832 (ii) -2744000

The function f( x ) = [x] + sqrt{{ x}} , where [.] denotes the greatest Integer function and {.} denotes the fractional part function respectively, is discontinuous at

Solve the following equations x^(2)-3-{x}=0 where [x] denotes the greatest integer and {x} fractional part.

Approach to solve greatest integer function of x and fractional part of x ; (i) Let [x] and {x} represent the greatest integer and fractional part of x ; respectively Solve 4{x}=x+[x]