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Growth of superexponential
#7
picture this.

consider a C^2 function f(x) with

1) f(0) = 1 and f ' (0) > 1.

2) for x > 0 : f ' (x) > 0 and f '' (x) > 0.

3) f(1) = b and b > 2.

As b gets larger , what can you say about f(1,001) ?

Do you think f(1,001) is bounded as b grows or not ?

Once you solved this , notice how sexp_b(x) can be such a function if we set the conditions C^2 and 1) , 2) and 3).

Also notice that if we modify the conditions such that f ' (0) = 1 AND f '' (0) > 0 we get the same result.

( We do not get weird limits because of the property C^2 )

regards

tommy1729
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Messages In This Thread
Growth of superexponential - by Balarka Sen - 02/26/2013, 11:19 AM
RE: Growth of superexponential - by tommy1729 - 02/26/2013, 10:00 PM
RE: Growth of superexponential - by Balarka Sen - 02/27/2013, 02:19 PM
RE: Growth of superexponential - by sheldonison - 02/27/2013, 06:40 PM
RE: Growth of superexponential - by Balarka Sen - 02/27/2013, 07:24 PM
RE: Growth of superexponential - by tommy1729 - 03/01/2013, 12:11 AM
RE: Growth of superexponential - by tommy1729 - 03/06/2013, 11:51 PM
RE: Growth of superexponential - by tommy1729 - 03/06/2013, 11:55 PM

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