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Question

Find the value oflimx 2[x], where [x] represents greatest integer less than or equal to x.


  1. 2

  2. 3

  3. None of these

  4. 1


Solution

The correct option is C

None of these


lets look at the greatest integer before we solve this. The graph of [x] looks like.

We can see that  the garph breaks at every integer points.

We want to find limx 2[x]

We will find left hand limit (limx 2f(x)) and Right hand limit (limx 2+f(x)) separately, because the

garph breaks at the point where we want to find the limit.

(limx 2f(x))=limh 0f(2h)=1 
(limx 2+f(x))=limh 0f(2+h)=2
Since, Both limits are not equal the limit doesn't exist.
Note - In greatest integer function limit doesn't exist at any integer point.

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