AOD application

Calculus Level 3

e π … π e e ^ \pi \ldots \pi ^ e

Fill in the blanks (plz don't use calculator, try by considering a function)

cannot predict almost equal < = >

Tanishq Varshney by Tanishq Varshney , 23, India

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2 solutions

Tanishq Varshney
Jan 23, 2015

CONSIDER

note its π π e π \pi^{\frac{\pi e}{\pi}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Rimba Erlangga
Jan 23, 2015

e π . . . π e e^{\pi} ... \pi^e

= l o g e π e . . . π = log_{e} \pi^e ... \pi

= l o g e π . . . π e = log_{e} \pi ... \frac{\pi}{e}

= l o g e ( e + x ) . . . e + x e = log_{e} (e + x) ... \frac{e + x}{e}

= 1 , 1... > 1 , 0... = 1,1... > 1,0...

I use my own lemma that l o g a b > a b log_a b > \frac{a}{b} for any a < b a < b

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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