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Topic: stumped by a limit
Replies: 1   Last Post: Nov 11, 2013 7:14 AM

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Sean McIlroy

Posts: 12
Registered: 1/7/11
stumped by a limit
Posted: Oct 26, 2013 9:46 AM
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hello all

i'd like to evaluate

lim_{x,y -> 0} [ f(x,y) / g(x,y) ]

where

f(x,y) = arccos [ (cos x)(cos y) + k(sin x)(sin y) ]

g(x,y) = [ (sin x)^2 - 2k(sin x)(sin y) + (sin y)^2 ]^(1/2)

on geometric grounds i suspect that this limit is unity for any /k/ <= 1;
anyway i'm stumped; if anybody can give me a hint, or point me toward a useful
text, it would be sure much appreciated

peace
stm



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