Which of the following functions are continuous x>1 ? [Note: Where [k] denotes greatest integer function less than or equal to k and k denotes fractional part function of k .]

Step-by-step solution

Check at x=k k I (a) . array l f (k⁺ )=k f (k⁻ )=k-1+1=k array ] continuous (b) aligned f (k⁺ ) & =k^2+0+2 k 0=k^2 f (k⁻ ) & =(k-1)^2+1+2+2(k-1)(1)=k^2 aligned (c) for x>1 x is less than e^x and both function are positive. x>1 0 < x e^x < 1 []=0 continuous (d) aligned & f (k⁺ )=0 & f (k⁻ )=[] 0=0 continuous aligned