(22 points): sketch (by hand) the root locus with respect to k for the equation 1 + kl(s) = 0 and the listed choices for l(s). be sure to give the asymptotes, and the arrival and departure angles at any complex zero or pole. you may check your sketch with matlab, but do not submit matlab plots. (a) l(s) = 2 s(s + 1)(s + 5)(s + 10) (b) l(s) = (s + 3) s(s + 1)(s + 5)(s + 10) (c) l(s) = (s + 2)(s + 4) s(s + 1)(s + 5)(s + 10) (d) l(s) = 1 s 2 + 3s + 10 (e) l(s) = 1 s(s 2 + 3s + 10) (f) l(s) = s 2 + 1 s(s 2 + 4) (g) l(s) = 1 s 2(s + 8) (h) l(s) = 1 s 3(s + 8) (i) l(s) = 1 s 4(s + 8) (j) l(s) = s + 3 s(s + 10)(s 2 + 2s + 2) (k) l(s) = [(s + 1)2 + 1] s 2(s + 2)(s + 3)