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Getting Cubic With Limits (Posted on 2008-02-09) Difficulty: 2 of 5
Determine all possible real t that satisfy this relationship:

Lim (5p + 7p + 11p)1/p = t3 - t + 5
p→∞

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Solution Here it is | Comment 1 of 2

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
  Posted by FrankM on 2008-02-09 13:38:50

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