1.

Let `[x]`be the greatest integer less than or equal to `xdot`Then, at which of the following point (s) function `f(x)=xcos(pi(x+[x]))`is discontinuous?(a)`x=1`(b) `x=-1`(c) `x=0`(d) `x=2`

Answer» `f(x)=xcosx(pi(x+[x]))`
`f(x)=xcos(pix+pi[x])`
`f(x)=(-1)^[[x]] xcospix`
`lim_(x->o^-)f(x)=lim_(x->0^-)f(x-4)=(x-h)cos(pi(x-h+[x-h]))`
`=-hcos(pi(-h-1))`
`=-hcos(pih+pi)`
`=0`
`lim_(x->0^+)=lim_(x->o^+)f(x+h)=(x+h)cos(pi(x+h+[x+h]))`
`=hcospih=0`
Correct option is A,B and D.


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