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Question

limx1x-1, where [.] is the greatest integer function, is equal to

(a) 1 (b) 2 (c) 0 (d) does not exist

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Solution

We have,

limx1-x-1=limh01-h-1=limh0-h=-1 (k − 1 < k − h < k ⇒ [k − h] = k − 1, k ∈ Z)

Also,

limx1+x-1=limh01+h-1=limh0h=0

limx1-x-1limx1+x-1

Thus, limx1x-1 does not exist.

Hence, the correct answer is option (d).

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