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If \mathrm{f}(\mathrm{x})=0, for [x]=0 then \lim _{x \rightarrow 0} f(x) where [.] denoted the greatest integer function.

Option: 1

equal to 1


Option: 2

equal to 0


Option: 3

does not exist


Option: 4

none of these


Answers (1)

best_answer

\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{-}} \frac{\sin [x]}{[x]}=\frac{\sin (-1)}{(-1)}=\sin 1

and =0 as it is given that f(x)=0 for [x]=0

So, \lim _{x \rightarrow 0} f(x) doesn't exist.

Hence (c) is the correct answer.

Posted by

shivangi.bhatnagar

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