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Which is Bigger?

23 May 18
Sukrit Vijaykar
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Sum fun things about numbers courtesy my friend Srinivas Shastri a very wise lover of maths

There was this question once asked in JEE

Which is greater? e^π or π^e?

The solution to this problem is simple yet elegant

The trick is to see that the function x^(1/x) is max when x=e. So:

e^(1/e) > π^(1/π)

Raising both sides to eπ, we get:

From our IIT-JEE 1981 Math paper
with a doff to Feynman.QED

 

 

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