Find lim (-1)^[x] x->2 [x] is the greatest integer function

[lizzie]

find
lim (-1)^[x]
x->2

[x] is the greatest integer function
-> means tends to

thanks to any help.

 

[CompuChip]

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.

 

[HallsofIvy]

find
lim (-1)^[x]
x->2

[x] is the greatest integer function
-> means tends to

thanks to any help.

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?

 

[aniketp]

find
lim (-1)^[x]
x->2

[x] is the greatest integer function
-> means tends to

thanks to any help.

Looks to me that the limit does not exist.
There are different answers for the +ve and -ve limit.

 

[CompuChip]

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?

 

[HallsofIvy]

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.

 

[CompuChip]

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