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#1 2008-04-27 20:02:18
- Janiffer
- Member
- Registered: 2008-04-26
- Posts: 12
Exponential and logarithmic functions
how do you show that
lnx<(x^1/2) x>0...
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#2 2008-04-28 00:39:59
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: Exponential and logarithmic functions
Hence f(x) has a minimum at x = 4. Also, since f(x) → +∞ both as x → 0[sup]+[/sup] and as x → +∞, and f(x) is continuous and has no other critical points, this minimum is a global minimum.
Finally, note that f(4) = 2 − 2ln2 > 0 (since ln2 < 1). Since the minimum value of f(x) is positive, we can conclude that f(x) > 0 for all x > 0.
Theres probably a smarter method to do this. Mathsyperson? Ricky?
Last edited by JaneFairfax (2008-04-28 00:41:52)
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#3 2008-04-28 06:33:27
- mathsyperson
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- Registered: 2005-06-22
- Posts: 4,900
Re: Exponential and logarithmic functions
That's the way I'd do it. (Well, my first thought was induction, but that's obviously wrong)
Why did the vector cross the road?
It wanted to be normal.
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