Thomas Calculus 13th [Solutions]

932 Chapter 13 Vector-Valued Functions and Motion in Space
d u
34. u C ai bj ck with a, b, c real constants da
i
db
j
dc
k
dt dt dt dt
0i 0j 0k
0
35-38. Example CAS commands:
Maple:
> with( plots );
r : t - [sin(t)-t*cos(t),cos(t) t*sin(t),t^2];
t0 : 3*Pi/2;
1o : 0;
hi : 6*Pi;
P1: spacecurve( r(t), t 1o..hi, axes boxed, thickness 3 ):
display( P1, title "#35(a) (Section 13.1)" );
Dr : unapply( diff(r(t),t), t ); # (b)
Dr(t0);
# (c)
q1: expand( r(t0) Dr(t0)*(t-t0) );
T : unapply( q1, t );
P2 : spacecurve( T(t), t 1o..hi, axes boxed, thickness 3, color black ):
display( [P1,P2], title "#35(d) (Section 13.1)" );
39-40. Example CAS commands:
Maple:
a : 'a'; b : 'b';
r : (a,b,t) - [cos(a*t),sin(a*t),b*t];
Dr : unapply( diff(r(a,b,t),t), (a,b,t) );
t0 : 3*Pi/2;
q1: expand( r(a,b,t0) Dr(a,b,t0)*(t-t0) );
T : unapply( q1, (a,b,t) );
1o : 0;
hi : 4*Pi;
P : NULL:
for a in [ 1, 2, 4, 6 ] do
P1: spacecurve( r(a,1,t), t 1o..hi, thickness 3 ):
P2 : spacecurve( T(a,1,t), t 1o..hi, thickness 3, color black ):
P : P, display( [P1,P2], axes boxed, title sprintf("#39 (Section 13.1)\n a %a",a) );
end do:
display( [P], insequence true );
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