Discussion Forum

1)

Let [X] be the greatest integer less than or equals to x. Then , at which of the following points(s) the function 

$f(x)=x\cos(\pi(x+[x]))$  discontinous?

Answer:

Option A,B,D

Explanation:

$f(x)=x\cos(\pi(x+[x]))$

  At x=0

   $\lim_{x \rightarrow 0}f(x)=\lim_{x \rightarrow 0}x\cos(\pi(x+[x])=0$

   and f(x)=0

 It is continous at x=0 and clearing discontinous at other integer points