Greatest integer function limit problem. Proving whether the limit exists

[johnjrgs]

Homework Statement

Prove that the limit exists.
lim 5 - 1/2[[2x]]
x-->1
Show your solution..

Homework Equations

The Attempt at a Solution

Tried getting the limit from the right and left.. not sure if what I've done is right though but this is what I got.

lim 5 - 1/2[[2x]] ===> 5-1/2(2(1)) ====> 4
x-->1+

lim 5 - 1/2[[2x]] ===> 5-1/2(2(1)) ====> 4
x-->1-

The answer I got is equal in both ways, therefore the limit exists.

If I'm wrong tell me where and help me please.

 

[HallsofIvy]

It would help if you told us what [[x]] meant! I thought it might be the "floor function" but if that were true then for 0< x< 1, [[2x]] would be 0, not 2, so the lower limit would be 5, not 4.