Finite Playground

To verify is human; to prove, divine.

Cute calculus puzzle

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Let

f(x) = \mathrm{arctan}(x) + \mathrm{arctan}(1/x).

What is \frac{d}{dx}f(x)?  What does it say about f(x)?  Try to calculate some values of f(x) and explain.

Author: hcsoso

Ph.D. student in the Department of Computer Science, University of Illinois at Urbana-Champaign.

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