Prove that

for all .

* Proof. * We consider two cases:

Case #1: If then for all so,

The final equality follows since for .

Case #2: If . Then for all . So,

since for all

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Stumbling Robot

A Fraction of a Dot
#
Find an integral formula involving the absolute value function

Prove that

for all .

* Proof. * We consider two cases:

Case #1: If then for all so,

The final equality follows since for .

Case #2: If . Then for all . So,

since for all