(a) Use a computer algebra system to graph the vector-valued function This surface is called a Mbius...

(a) Use a computer algebra system to graph the vector-valued function

This surface is called a Möbius strip.
(b) Is the surface orientable? Explain why or why not.

(c) Use a computer algebra system to graph the space curve represented by r(u, 0). Identify the curve.

(d) Construct a Möbius strip by cutting a strip of paper, making a single twist, and pasting the ends together.
(e) Cut the Möbius strip along the space curve graphed in part (c), and describe the result.

Transcribed Image Text:

r(u, v) = (4 v sin u) cos(2u)i + (4- v sin u) sin(2u)j + v cos uk, 0≤u≤ π, -1 ≤ y ≤ 1.