I need show that f(x)= x^2 +2 is continuous at x=3.
So I'm trying to prove that as x approaches 3 from the left = the value as x approaches 3 from the right.
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Vorsah
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- 22-10-2015 22:55
Last edited by Vorsah; 22-10-2015 at 22:57. -
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- 22-10-2015 22:57
The other one is upside down
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Indeterminate
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- 22-10-2015 23:56
(Original post by Vorsah)
The other one is upside down
The definition of continuity states that
and the epsilon-delta version is
So this is what you should be after
It should be easy for you to bound that by using the difference of two squares. That will give you delta in terms of epsilon.Last edited by Indeterminate; 23-10-2015 at 00:27. -
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- 23-10-2015 00:13
(Original post by Indeterminate)
That's not the way to prove continuity. You can have functions whose left and right hand limits agree at points where the "ordinary" limit is something completely different (i.e there's a discontinuity).
The definition of continuity states that
and
which is what he is trying to prove, I think.
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- 23-10-2015 00:19
(Original post by atsruser)
But that's equivalent toand
which is what he is trying to prove, I think.
EDIT: I've edited my post above to incorporate this.Last edited by Indeterminate; 23-10-2015 at 00:27.
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