Evaluating Limits?

[jkovie]

Lim[x]/x as x approaches 0+
The answer for this problem is supposed to be 0, why isn't it 1? Wouldn't the variables cancel out and just leave 1?
When I plug in zero, I just get the indeterminate 0/0. Any hints or suggestions pointing me in the right direction would be appreciated.
Thanks!

 

[Deleted member 4993]

Lim[x]/x as x approaches 0+
The answer for this problem is supposed to be 0, why isn't it 1? Wouldn't the variables cancel out and just leave 1?
When I plug in zero, I just get the indeterminate 0/0. Any hints or suggestions pointing me in the right direction would be appreciated.
Thanks!

What is [x]?

 

[HallsofIvy]

Lim[x]/x as x approaches 0+
The answer for this problem is supposed to be 0, why isn't it 1? Wouldn't the variables cancel out and just leave 1?
When I plug in zero, I just get the indeterminate 0/0. Any hints or suggestions pointing me in the right direction would be appreciated.
Thanks!

I suspect that you mean \(\displaystyle \lfloor x \rfloor\) which is defined as "the largest integer less than or equal to x". If x is positive but close to 0 (less than 1) then [itex]\lfloor x \rfloor= 0[/itex] so
\(\displaystyle \lim_{x\to 0} \frac{\lfloor x\rfloor}{x}= \lim_x\to 0 \frac{0}{x}= 0\).