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I'm sure I could think my way through these, but I'm sick and on a tight schedule, so I was hoping someone here could help me out. I would appreciate a verification, with or without proof, of the following assertions:
[tex]
(\mathcal O(\epsilon))^2 = \mathcal O(\epsilon^2)
[/tex]
and
[tex]
\sqrt{1 + \mathcal O(\epsilon^2)} = 1 + \mathcal O(\epsilon^2)
[/tex]
Thanks so much.
[tex]
(\mathcal O(\epsilon))^2 = \mathcal O(\epsilon^2)
[/tex]
and
[tex]
\sqrt{1 + \mathcal O(\epsilon^2)} = 1 + \mathcal O(\epsilon^2)
[/tex]
Thanks so much.