Suppose that exist and is positive. Show that for any positive integer n we have

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- Apr 16th 2009, 12:12 PMmancillaj3real hard problem
Suppose that exist and is positive. Show that for any positive integer n we have

. - Apr 17th 2009, 12:28 PMOpalg
Those are meant to be n'th roots, right? ?

The slick way to do this is to say that is just the composition of the function f with the n'th root function . The function g(t) is continuous at all points t>0 (because in fact it is differentiable, with derivative ). And the composition of two continuous functions is continuous. So the function is continuous at (where is defined to be ). - Apr 18th 2009, 07:17 PMmancillaj3
thank you, is there another way to approach it?

- Apr 19th 2009, 07:45 AMOpalg