Evaluate lim x-->infinity [x]/x and lim--> -infinity [x]/x.
The Attempt at a Solution
The think the limits for both of these are 1. I also know that [x] is the largest integer not greater than x.
I think that I can use the squeeze theorm to say that x-1/x <[x]/x <equal to 1. Does this arguement work for both limits or should I prove this an alternate way?