$lim x \to 3 ([x - 3] + [3 - x] - (x))$ , where [.] denotes the greatest integer function, is equal to

4

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- 4

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Solution

The correct option is B $- 4$
Left hand limit $= lim x \to 3^{-} ([x - 3] + [3 - x] - (x)) = - 1 + 0 - 3 = - 4$
and Right hand limit $= lim x \to 3^{+} ([x - 3] + [3 - x] - (x)) = 0 - 1 - 3 = - 4$
Therefore, required limit value is $- 4$
Hence, option 'B' is correct.

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