$l i m x \to 3 ([x - 3] + [3 - x] - x), where[.]denote the greatest integer function, is equal to:$

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-4

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Does not exist

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Solution

The correct option is B
-4

$R . H . L = l i m h \to 0 ([(3 + h) - 3] + [3 - (3 + h) - (3 + h)) = l i m h \to 0 ([h] + [- h] - 3 - h) = l i m h \to 0 (0 - 1 - 3 - h) = - 4 L . H . L = l i m h \to 0 ([(3 - h) - 3] + [3 - (3 - h) - (3 - h)) = l i m h \to 0 ([- h] + [h] - 3 + h) = l i m h \to 0 (- 1 + 0 - 3 + h) = - 4 L.H.L=R.H.L ∴ l i m x \to 3 ([x - 3] + [3 - x] - x) = - 4$

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