Balanced derivative?
From: helopticor (loqstuy_at_hotmail.com)
Date: 07/17/04
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Date: 17 Jul 2004 06:52:23 -0400
d/dx(Abs(x))|x=0 is undefined. But lim h->0 ((abs(0+h)-abs(0-h))/(2h))
IS defined. is there a name for this derivative like quotient in
general?,( i.e. : lim h->0 ((f(x+h)-f(x-h))/(2h))) has anyone studied
it with or without naming it? Is it always equal to the regular
derivative whenever the regular derivative is defined? Please respond
even it's just to say that no one has named it or looked at it.
[
Moderator's Note.
Yes, "symmetric derivative" is the usual name. A Google search produced
three references to get you started:
<http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2002&task=show_msg&msg=0197>
<http://www.science.edu.sg/ssc/detailed.jsp?artid=568&type=6&root=1&parent=1&cat=12>
C. E. Aull, The First Symmetric Derivative (in Classroom Notes)
American Mathematical Monthly 74 (1967) 708-711.
]
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