This is one of the high school math problems which Calculus can

This is one of the high school math problems in which Calculus can go much deeper.

Result: For each 0 < x < 1/e, there is a y in the interval (1/e, 1) such that x^x = y^y.

Proof:

Using Calculus, it is easy to verify that function f(x) = x^x decreases from 1 to its minimum f(1/e) as x goes from 0 to 1/e and that f(x) increases from f(1/e) to the positive infinity as x goes from 1/e to the positive infinity.The result then follows.

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• 这个深！连闺女来年上大学的解答都准备好了，呵呵。偷偷藏起来，等她明年此时来问我。（空） -thegreatcolour- ♀ (0 bytes) () 11/02/2011 postreply 06:56:51