By differentiating the equation b=tx n, derive the equation b' = -tn. (2) calculate the frenet apparatus (t, k, n, b, t) of the following curve a(t) = (1/2) (sint + cost), (1/2)e' (sint - cost), e) (3) check whether the following bases are positive: (a) the basis {(1,3), (4,2)} in rp (b) the basis {(1,3,5), (2,3,7), (4,8,3)} in r. (4) a circular disk of radius 1 in the (x, y) plane rolls without slipping along the r axis. the figure described by a point on the circumference of the disk is called a cycloid (figure 1-7 in the text). write the equation that describes a parametrized curve a: r → r², whose image is the cycloid. determine its singular points. (5) let (0 ) r2 he given by