Properties of Greatest Integer Function `(vi)[x]gekimplies xgek; where k epsilon Z (vii) [x]lek implies xlt(k+1); where kepsilonZ (viii) [x]gtk implies xgt(k+1)`; where `k epsilonZ`

Properties of Greatest Integer Function (ix) [x]

Properties of smallest integer function property (i)[-n]=-[n]where n epsilon N (ii) [-x]=-[x]+1; where xepsilon R-Z (iii) [x+n]=[x]+n where x epsilon R-Z and n epsilon Z (iv) [x]+[-x]={1; x notinZ ; 0 ; xinZ} (v) [x]-[-x]={2[x]-1; xnotinZ ; 2[x] ; if xinZ

If x+y =k , where x, y epsilon N then xy is maximum when (x, y)-=..

Find the left hand and right hand limits of greatest integer function f(x)=[x]= greatest integer less than or equal to x, at x=k, where k is an integer.

Let g(x)=sqrt(x-2k), AA 2k le x lt 2(k+1) where, k in l , then

If xy=k , where x, y epsilon N , then x+y is minimum when (x, y)-= …

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then

If the graph of f(x)=x^(2)+(3-k)x+k (where k varepsilon R ) lies above and below x-axis,then k cannot be (i)1(ii)0 (ii) -1 (iv) 10