[x] is the greatest integer function
-> means tends to
thanks to any help.
Start by plotting it. Then see if you can already find the limit from the graph. Only the final step is to try and prove it rigorously.
Looks straight forward to me. For all x larger than 1 but less than 2, [x]= 1 so the limit, as x approaches 2 from below is (-1)1= -1.
For x larger than 2 but less than 3, [x]= 2. So what is the limit as x approaches 2 from the above? And what does that tell you about the limit itself?
Looks to me that the limit does not exist.
There are different answers for the +ve and -ve limit.
Are aniketp and lizzie the same person? Or did you decide to just give away the answer after a week without reply from the OP?
After a week, I would suspect that the OP just can't be bothered to look at the responses and see nothing wrong with posting the answer- in case someone else is interested.
I agree, I just found it odd that someone who apparently has nothing to do with the thread posted this a week after the last message. I suppose on my list it would have dropped to page 40 or something by then
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