$lim x \to 2 {[2 - x] + [x - 2] - x}$ is equal to?
(where [x] is a greatest integer function )

0

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3

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- 3

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Does not exist

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Solution

The correct option is C $- 3$
${lim}_{x \to 2^{+}} {[2 - x] + [x - 2] - x}$
$= - 1 + 0 - 2 = - 3$
${lim}_{x \to 2^{-}} {[2 - x] + [x - 2] - x}$
$= 0 - 1 - 2 = - 3$
LHL $=$ RHL
${lim}_{x \to 2} {[2 - x] + [x - 2] - x} = - 3$

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