Pre-Calc Homework Solutions 22

# Pre-Calc Homework Solutions 22 - 22 Section 1.4 30 The...

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24. (a) [ 2 1, 5] by [ 2 1, 3] Initial point: (0, 2) Terminal point: (4, 0) (b) y 5 ˇ 4 w 2 w t w 2 w 5 ˇ 4 w 2 w x w The parametrized curve traces the right portion of the curve defined by y 5 ˇ 4 w 2 w x w , that is, for x \$ 0. 25. (a) [ 2 3, 3] by [ 2 2, 2] No initial or terminal point, since the t -interval has no beginning or end. The curve is traced and retraced in both directions. (b) y 5 cos 2 t 5 cos 2 t 2 sin 2 t 5 1 2 2 sin 2 t 5 1 2 2 x 2 52 2 x 2 1 1 The parametrized curve traces the portion of the parabola defined by y 52 2 x 2 1 1 corresponding to 2 1 # x # 1. 26. (a) [ 2 4, 5] by [ 2 4, 2] Initial point: None Terminal point: ( 2 3, 0) (b) x 5 t 2 2 3 5 y 2 2 3 The parametrized curve traces the lower half of the parabola defined by x 5 y 2 2 3 (or all of the curve defined by y 52 ˇ x w 1 w 3 w ). 27. Using ( 2 1, 2 3) we create the parametric equations x 52 1 1 at and y 52 3 1 bt , representing a line which goes through ( 2 1, 2 3) at t 5 0. We determine a and b so
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