Unformatted text preview: −→ f ( t ) = ( x ( t ) ,y ( t ) ,z ( t )) is diFerentiable at t = t precisely if all of its component functions are diFerentiable at t = t , and then v f ′ ( t ) = ( x ′ ( t ) ,y ′ ( t ) ,z ′ ( t )) . In particular, every diFerentiable vectorvalued function is continuous. When −→ p ( t ) describes a moving point, then its derivative is referred to as the velocity of −→ p ( t ) −→ V ( t ) = ˙ −→ p ( t ) and the derivative of velocity is acceleration −→ a ( t ) = ˙ −→ V ( t ) = ¨ −→ p ( t ) . The magnitude of the velocity is the speed , sometimes denoted d s dt = b −→ V ( t ) b ....
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 Fall '08
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 Calculus, Derivative, Continuous function, Vectorvalued function

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