Limit involving floor function

[MathSquareRoo]

Homework Statement

Evaluate lim x-->infinity [x]/x and lim--> -infinity [x]/x.

Homework Equations

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 theorem to say that x-1/x <[x]/x <equal to 1. Does this argument work for both limits or should I prove this an alternate way?

 

[Dick]

Homework Statement

Evaluate lim x-->infinity [x]/x and lim--> -infinity [x]/x.

Homework Equations

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 theorem to say that x-1/x <[x]/x <equal to 1. Does this argument work for both limits or should I prove this an alternate way?

For one thing you should use parentheses if you don't want to use TeX. x-1/x is not the same as (x-1)/x and I think you meant (x-1)/x. For another show us how you got that inequality for x>0. And finally you should be able to figure out if it works for x<0. Try x=(-1/2). What went wrong??