This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: dsdt := (1)
(4 (cos(3 t) +sin(t))2 (—3 sin(3 t) +cos(t))2 +9 (cos(3 t) —cos(t))4(
1/2 [> dsdt == N07m(diff(Q(t)a t) ); —3 sin(3 t) +sin(t) )2 + (3 005(3 t) +3 cos(t) )2) > Length := evalf(1nt(dsdt, t=0 ..2Pi ' \/
Length := 45.97703316 (2) > evalf(subs(t=2, Curvature( ( (cos(3 * t) + sin(t) )A2, (cos(3 * t) cos(t) )A3, sin(3 * t) + 3 I: * Shim) ) ))
m (3)
l> plot(Curvature(Q(t), t), t=0 ..2'Pi); V evalf(subs(t—. Q(t) ) ); . .
2027 1526)ex + (3.642323710)ey +‘ s(2.704185087)ez ~ TM) Ivy/1b Wm“ (4) (t) ) ); Wm WM WWW/Q
1095528)ex + (3.588243743 )ey + ( 2.667676736)ez (5) > The maximas occu at approximately t = .97 and t = 4.14
R352
( . 2 V evalf(subs(t=4.14,
.02 MCPI == plot3a’( [0.02202741526, 3.642323710, 2.704185087], x =1 ..1,y =1 ..1, style
= point, symbol = box, color = blue) : > > MCP2 == plot3d( [0.02211095528, 3.588243743, ~2.667676736], x =1 ..1,y =l ..1, style
= point, symbol = box, color = blue) : > CURVE == spacecurve( Q(t), t = 0 ..2 Pi, axes = normal, labels = [x, y, 2], color = black,
thickness = 2) : > display( {MCP1, MCP2, CUR VE}) ; T F . E t .
[
w [
[
[
l ﬂVllrh/m. I \hlﬂM/‘Pl/I @Yiﬁ Wawm
will \ > Spacecurvd Q”), t = 0 __2  Pi, axes = normal, color = black, thickness = 2, labels = [x, y, 2],
orientation = [0, 90]); ...
View
Full
Document
This note was uploaded on 04/04/2012 for the course CALC 251 taught by Professor Asbuch during the Spring '08 term at Rutgers.
 Spring '08
 asbuch
 Multivariable Calculus

Click to edit the document details