Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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#1 2012-10-27 19:46:42
- Harold
- Guest
Inequality with pi and e
What is the solution of this problem?and how is the problem solved-
#2 2012-10-27 20:26:19
- bobbym
- Administrator
Online
Re: Inequality with pi and e
Hi Harold;
This one has been around for a long time. The standard answer starts with raising both sides to the power of
after that it is a maxima-minima problem.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2012-10-27 20:50:54
- bobbym
- Administrator
Online
Re: Inequality with pi and e
Hi;
e^e is not greater than π^π. That is not what I said. You did something wrong with the first step.
From here it is an ugly calculus problem.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#6 2012-10-28 10:47:28
- scientia
- Full Member
Offline
Re: Inequality with pi and e
Let ; then when . So is decreasing for ; as , , i.e. .