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If f (x) = [x] – ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 4 x , x ∈ R, where [x] denotes the greatest integer function, then :

1. − → 4 x lim f (x) exists but + → 4 x lim f (x) does not exist.
2. Both − → 4 x lim f (x) and + → 4 x lim f (x) exist but are not equal.
3. + → 4 x lim f (x) exists but − → 4 x lim f (x) does not exist.
4. f is continuous at x = 4.

Correct answer: f is continuous at x = 4.

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