Re: Mathematical Question

[Etienne Grossmann]

  Hi all,

you can apply l'Hospital rule for second derivatives: iirc, if
A(z)=B(z)=A'(z)=B'(z)=0 and B''(z)!=0, then A(x)/B(x) tends to
A''(z)/B''(z) when x tends to z. You may need to check in your
favorite calculus book.

  Iigc, it is indeed (c-1)/2, except when c=0, in which case you get
+/-infinity.

  Hth,

  Etienne

On Mon, Aug 02, 2004 at 01:20:29PM -0700, Henry F. Mollet wrote:
# I have nowhere else to turn, I'm hoping the octave help
# list can provide a tip. Many thanks, Henry
# 
# y = x/(1-x) - cx^c/(1-x^c),
# where c is a positive integer constant
# 
# I need to know y in the limit as x approaches 1.
# I even have the result by biological reasoning
# and it is (c-1)/2 but how do I prove it mathematically?
# 
# For example using x = 0.999 and c = 100 we have:
# y = 999 - 950.4 = 48.6 whereas (c-1)/2 = 49.5;
# Using x = 0.9999 and same c = 100, we have:
# y = 9999 - 9949.6 = 49.4 whereas (c-1)/2 = 49.5, close enough.
#  
# Somehow I have to expand the second term in the
# expression into a series where the first term of the
# series will be the same as the first term of the
# expression (i.e. x/(1-x)) and they will cancel out.
# 
# In my application, the constant c is a positive integer,
# and that's what I used for empirical checks of the result
# but I have not checked if that's a requirement.
# 
# 
# 
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-- 
Etienne Grossmann ------ http://www.cs.uky.edu/~etienne



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