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stumped by a limit
Posted:
Oct 26, 2013 9:46 AM


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



