Determine all possible real
t that satisfy this relationship:
Lim (5p + 7p + 11p)1/p = t3 - t + 5
p→∞
11^p < 5^p + 7^p + 11^p < 3 x 11^p
11 < (5^p + 7^p + 11^p) ^(1/p) < 11 x 3^(1/p)
In the limit 3^(1/p) -> 1 so
11 = t^3 - t + 5 So t = 2. (The other roots are complex.)
Edited on February 9, 2008, 1:49 pm
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Posted by FrankM
on 2008-02-09 13:38:50 |