Unformatted text preview: ( x,f ( x )) equals the derivative of f ( x ) at x .) (b) Show that the vectorvalued function −→ p ( t ) = ( t  t  ,t 2 ) is C 1 and onetoone on the whole real line, but its image is the graph of the function y =  x  , which fails to be di²erentiable at x = 0. This shows the importance of the condition that the velocity is always nonzero in our de±nition of regularity. 9. Prove Remark 2.4.8 , as follows: Suppose C is parametrized by −→ p ( t ) = ( x ( t ) ,y ( t ) ,z ( t ))...
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 Fall '08
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 Calculus, Equations, Derivative, Vectorvalued function, vertical line test—so, regular vectorvalued function

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