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प्रश्न
Evaluate the following :
`lim_(x -> 0)[x]` ([*] is a greatest integer function.)
उत्तर
We know that
[x] = 0 if 0 < x < 1
= – 1 if – 1 < x < 0
∴ `lim_(x -> 0^+) [x] = lim_(x -> 0) 0` = 0
`lim_(x -> 0^-) [x] = lim_(x -> 0) (-1)` = – 1
∴ `lim_(x -> 0^+) [x] ≠ lim_(x -> 0^-) [x]`
∴ `lim_(x -> 0) [x]` does not exist.
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