Q. 8 Most of the parametric equations... [FREE SOLUTION]

Chapter 11: Q. 8 (page 859)

Most of the parametric equations and vector-valued functions we have studied have component functions that are continuous. What happens when one of the component functions is discontinuous at a point? For example, the 鈥渇loor鈥� function $z (t) = 鈱�t鈱�$ has a jump discontinuity for every integer $t$ . What is the graph of the equations $x = \cos 2 蟺 t, y = \sin 2 蟺 t, z = t, t 鈭� R$ ?

Expert verified

The image of the graph has been added below.

The floor function is $z (t) = 鈱�t鈱�$ , it has jump discontinuity for every integer $t$ .

As we know, the objective is to construct a graph when one component is discontinuous at a point
Take an example of circular helix

$r (t) = <\cos 2 蟺 t, \sin 2 蟺 t, 鈱�t鈱�>$
$x (t) = \cos 2 蟺 t . . . . . . (1)$
$y (t) = \sin 2 蟺迟 . . . . . . (2)$
$z (t) = 鈱�t鈱� . . . . . . (3)$

A table of different values of $t$

Image of the graph.

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with 91影视!

All the tools & learning materials you need for study success - in one app.

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.