Which is Greater?Date: 2/12/96 at 21:37:0 From: Raul Daniel Digestani Subject: Help Please help me to solve the following problem: Let be A = 10001^9999 and B = 10000^10000 - Which is greater? Why? Thanks. Raul Daniel Digestani Buenos Aires - Republica Argentina Date: 9/1/96 at 18:36:36 From: Doctor James Subject: Re: Help Let B = 10000^10000=10000 * 10000^9999 We can use the approximation f(x+h) ~= f(x) + d(f(x))/dx * h, where x = 10000 and h=1, and f(x) = x^9999 d(f(x))/dx = 9999 * x^9998, so f(1001) ~= 10000^9999 + 9999 * 10000^9998 * 1, where ~= means approximately ~= 10000^9999 + 10000 * 10000^9998 equal to. = 10000^9999 + 10000^9999 = 2 * 10000^9999, which is much less than 10000^10000 = 10000 * 10000^9999. So B > A. -Doctor James, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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