Current Events > How do you go about finding the limit x->infinity of x/[x] ?

(+) Yeah! (+)

Where [x] is the greatest integer function. Sure it's easy to guess plugging in different numbers. But how do you go about actually proving it?

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Try boxing it between 2 functions that both have the same limit as x->infty

Unless I'm missing something, the limit should be 1(?)

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Are you talking about a proof proof or do you just want to solve it?

Because the limit of any undefined formula that evaluates to 0*infinity, infinity/infinity, or 0/0 is equivalent to the limit of it's derivative.

So you take dy/dx of x/[x] and then solve for that limit. Repeat again if you must.

That requires you to take my word for it. Proving it is much more advanced.

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LordFarquad1312 posted...

Try boxing it between 2 functions that both have the same limit as x->infty

Unless I'm missing something, the limit should be 1(?)

If [x] = x you're correct. If [x] = 2x the limit is 1/2, if it's x^2 the limit is 0.

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