Pre-Calc Homework Solutions 18

Pre-Calc Homework Solutions 18 - 18 Section 1.4 Exploration...

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4. 0 # t # } p 2 } : [ 2 6, 6] by [ 2 4, 4] 0 # t # p : [ 2 6, 6] by [ 2 4, 4] 0 # t # } 3 2 p } : [ 2 6, 6] by [ 2 4, 4] 0 # t # 4 p : [ 2 6, 6] by [ 2 4, 4] Let d be the length of the parametric interval. If d , 2 p , you get } 2 d p } of a complete ellipse. If d 5 2 p , you get the complete ellipse. If d . 2 p , you get the complete ellipse but portions of the ellipse will be traced out more than once. For example, if d 5 4 p the entire ellipse is traced twice. 5. 0 # t # 2 p : [ 2 6, 6] by [ 2 4, 4] initial point: (5, 0) terminal point: (5, 0) p # t # 3 p : [ 2 6, 6] by [ 2 4, 4] initial point: ( 2 5, 0) terminal point: ( 2 5, 0) } p 2 } # t # } 3 2 p } : [ 2 6, 6] by [ 2 4, 4] initial point: (0, 2 2) terminal point: (0, 2) Each curve is traced clockwise from the initial point to the terminal point. Exploration 3 Graphing the Witch of Agnesi 1. We used the parameter interval [0, p ] because our graphing calculator ignored the fact that the curve is not defined when t 5 0 or p . The curve is traced from right to left
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