Need help proving something.

Show using the definition of a limit that lim (as x approaches c) of (x^3)=(c^3) for all c in R.

Thank you in anticipation.

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- Oct 30th 2006, 04:16 PMFares23Limit Definition
Need help proving something.

Show using the definition of a limit that lim (as x approaches c) of (x^3)=(c^3) for all c in R.

Thank you in anticipation. - Oct 30th 2006, 05:34 PMThePerfectHacker
If then,

For every

There is

such as,

if is in domain,

then,

.

The first inequality can be expressed as,

And,

Thus,

If you chose,

Thus,

Would make the inequality work can gaurentte the function is defined.

Now you do the second half if, .

There got to be a more simple way to do it. But that is the only one that I came up with. - Oct 30th 2006, 09:51 PMFares23
You don't have to write out the whole thing, but what changes for c<0?

- Oct 31st 2006, 05:25 AMThePerfectHacker
- Oct 31st 2006, 03:35 PMFares23
What did you do wrong in the first part?

- Oct 31st 2006, 05:59 PMThePerfectHacker