e^(Pi) vs (Pi)^e

Posted: February 28, 2016 in Calculus: An Introduction
Tags: , ,

Is  e^π > π^e  or  is  e^π < π^e ???

This is a continuation of my Euler-pi theme that seems to have consumed me over the past two days. The answer to the question put forth is easy to determine using technology but little to nothing of value is learned through that process. Natural logarithms, functions and derivatives are once again employed here to arrive at a logical (to me) conclusion.
e and pi
e vs pi2

 

Click on the link provided here for an exploration of the tangent line as it moves along the function.

This entry opens a discussion on “local” versus “global” extrema as well as indeterminate limits.

Click on L’Hospital’s Rule to see the limit of  x/ln(x)  as  x→∞.

 

Thanks for reading.

 

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