> #11.7\
# plots not included\
with(plots): with(linalg):
> #1\
spacecurve([cos(4*t),t,sin(4*t)],t=0..2*Pi,numpoints=100);
> #5\
spacecurve([cos(t),sin(t),sin(5*t)],t=0..2*Pi,numpoints=100);
> #9\
spacecurve([sin(t),3,cos(t)],t=0..2*Pi,numpoints=100);
> #13\
spacecurve([t^2,t^4,t^6],t=0..2,numpoints=100);
> #25\
[limit(sqrt(t+3),t=1),limit((t-1)/(t^2-1),t=1),limit(tan(t)/t,t=1)];

                                [2, 1/2, tan(1)]
> #29\
diff( [1,tan(t),sec(t)], t);

                                       2
                         [0, 1 + tan(t) , sec(t) tan(t)]
> #33\
 diff(a+b*t+c*t^2,t);

                                    b + 2 c t
> #37\
r:=t->[1+t,t^2];\
rprime:=unapply(diff(r(t),t),t);\
rprime(1);

                                                 2
                              r := t -> [1 + t, t ]

                             rprime := t -> [1, 2 t]

                                     [1, 2]
> #41\
r:=t->[2*t,3*t^2,4*t^3];\
rprime:=unapply(diff(r(t),t),t);\
T:=unapply(rprime(t)/norm(rprime(t),2),t);\
T(1);

                                              2     3
                           r := t -> [2 t, 3 t , 4 t ]

                                                     2
                         rprime := t -> [2, 6 t, 12 t ]

                                                     2
                                        [2, 6 t, 12 t ]
                  T := t -> 1/2 -------------------------------
                                             2            4 1/2
                                (1 + 9 abs(t)  + 36 abs(t) )

                                                1/2
                              1/92 [2, 6, 12] 46
> #45\
x0 := [1,1,1];\
rprime:=unapply(diff([t,t^2,t^3],t),t);\
dirvector:=rprime(1);\
eqns:=[x,y,z]=x0+scalarmul(dirvector,t);

                                 x0 := [1, 1, 1]

                                                     2
                          rprime := t -> [1, 2 t, 3 t ]

                             dirvector := [1, 2, 3]

                 eqns := [x, y, z] = [1, 1, 1] + [ t, 2 t, 3 t ]