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Engineering Calculus Notes 164

Engineering Calculus Notes 164 - 152 CHAPTER 2 CURVES =0 =...

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152 CHAPTER 2. CURVES θ = 0 θ = 2 π Figure 2.21: Cycloid pair of equations. By contrast, the dynamic view of a curve as the path of a moving point—especially when we use the language of vectors—extends very naturally to curves in space. We shall adopt this latter approach to specifying a curve in space. The position vector of a point in space has three components, so the (changing) position of a moving point is specified by a function whose values are vectors in R 3 , which we denote by −→ p : R R 3 ; this can be regarded as a triple of functions: x = x ( t ) y = y ( t ) z = z ( t ) or −→ p ( t ) = ( x ( t ) ,y ( t ) ,z ( t )) . As before, it is important to distinguish the vector-valued function
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