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Unformatted text preview: 1.3-Vector-Valued Functions and Parametrized Curves Idea of a Vector Function/Parametrized Curve: Eliminating the Parameter Vector and Parametric Equations of a Line Examples: 1 3 Given r(t) = (t 2 + 1)i + t 2 j: a) Find r(4) and r(t + h) b) Eliminate the parameter and sketch the graph Describe the motion of a particle whose position is given by x = -4 cos t, y = 3 sin t, 0 t Find vector and parametric equations of the line passing through the points (-1, 3) and (5, 2) Eliminate the parameter to sketch the graph of the vector function r(t) = ti + (t - 1)3 j. Does this graph differ from the first example? How? On Your Own: #1,3,5,7,9,15,17,25,27,29,31,34,35 ...
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