(A) Sketch the Curves Represented By:
(I) X = T/2 $1 - \frac { t ^ { 2 } } { 4 }$

Essay

(a) Sketch the curves represented by:
(i) x = t/2, y = $1 - \frac { t ^ { 2 } } { 4 }$ (ii) x = sin t, y = 1 sin $2$ t
(iii) x = e $t$ , y = 1 - e $2 t$ (b) Describe the differences between the three curves in part (a).(c) Produce Cartesian equations for the curves in parts (a)(i), (ii), and (iii) by eliminating the parameter. Compare your results.