limit problem

mahmoudaljamel · 2006-10-30 19:36:34

f(x) =X² if x is rational , 0 if x is irrational

Prove that lim f(x) as x approaches 0 is equel to 0

Dross · 2006-10-31 00:46:50

Now observe that:

So a useful choice for delta would be

.

Now you can show that the above is true:

mahmoudaljamel · 2006-11-01 01:56:58

what a great job Dross !

Is there any other way to prove without using the epsilon - delta defenition!? .

Dross · 2006-11-02 01:14:17

Depends on how rigorous you have to be - I suppose you could say that, if you are allowed to use the facts that:

and:

Then since f(x) alternates between x[sup]2[/sup] and 0, the result follows. Whether this would be acceptable depends on what you're supposed to know and how rigorous you're supposed to be, though.

Math Is Fun Forum

#1 2006-10-30 19:36:34

limit problem

#2 2006-10-31 00:46:50

Re: limit problem

#3 2006-11-01 01:56:58

Re: limit problem

#4 2006-11-02 01:14:17

Re: limit problem

Board footer