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quiz_04A - Math 213 Quiz 4 Name Solution d 1 |r(t)| = r(t...

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Unformatted text preview: Math 213 -- Quiz 4 Name Solution d 1 |r(t)| = r(t) r (t). dt |r(t)| 1. If r(t) = 0 show that By the Dot-Product Rule, d d (|r(t)|2 ) = (r(t) r(t)) = r (t) r(t) + r(t) r (t) = 2(r (t) r(t)). dt dt On the other hand, by the Chain Rule, d d (|r(t)|2 ) = 2|r(t)| |r(t)|. dt dt Therefore, d 2(r (t) r(t)) 1 |r(t)| = = r(t) r (t). dt 2|r(t)| |r(t)| as claimed. ...
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