Math 4A Delta College Calcplot 3D Labs

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Math 4A CalcPlot3D Lab 03
Topic: Vector-valued Functions and Graphing a Space Curve
Go to the website to access the CalcPlot3D app.
CalcPlot3D – Monroe Community College
https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/
Objective: The goal of Lab 03 show how CalcPlot3D constructs space curves and demonstrate how to
trace and display its path.
Here is a video that will demonstrate how to plot space curves using CalcPlot3D:

Apply what you have learned in the first two labs on plotting
surfaces along with the video for plotting space curves and
reproduce the image in section 12.1, example 4 on page 822.
Lab 03 DUE DATE is set in the Assignment
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Math 4A CalcPlot3D Lab 03 (A Week 02Topic Assignment)
Topic: Vector-valued Functions, Unit Tangent, Unit Normal, Unit Binormal
Go to the website to access the CalcPlot3D app.
CalcPlot3D – Monroe Community College
https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/
Objective: The goal of Lab 03 show how CalcPlot3D constructs space curves, trace the path of the curve,
and display the Frenet frame using its vector-valued function plotting capabilities
Here is a video that will demonstrate how to plot space curves using CalcPlot3D:
https://www.youtube.com/watch?v=YYftS8Kyvnk and discover how to display the Frenet Frame (or TNB-frame).
Use the space curve capabilities of CalcPlot3D to display
the space curve of the vector-valued function defined by
𝑟(𝑡) = (sin 𝑡 − 𝑡 cos 𝑡) 𝒊⃗ + (cos 𝑡 + 𝑡 sin 𝑡) 𝒋⃗ + 𝑡 ⃗𝒌⃗
and display at 𝑡 = 5 , the unit tangent vector, the unit
normal vector, and the unit binormal vector.
Lab 04 DUE DATE is set in the Assignment
4
= 1-
EXAMPLE 4 Representing a Graph: Vector-Valued Function
Sketch the space curve C represented by the intersection of the semiellipsoid
x2 2 2
1, 220
12 24
and the parabolic cylinder y = x2. Then find a vector-valued function to represent the
graph.
Solution The intersection of the two surfaces is shown in Figure 12.5. As in
Example 3, a natural choice of parameter is x = t. For this choice, you can use the
given equation y = xto obtain y = 12. Then it follows that
222
– 1 / 름
14_24 – 2r- r* _6 + 1)(4 – 1)
12
24
Because the curve lies above the xy-plane, you should choose the positive square root
for z and obtain the parametric equations
(6 + 12)(4 – 12)
*= 1, y = 1, and z =
The resulting vector-valued function is
(6 + 2)(4 – 12)
r(t) = ti + t?j +
-k, -2 sis 2.
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Vector-valued function
(Note that the k-component of r(t) implies -2 51 2.) From the points (-2,4, 0)
and (2, 4, 0) shown in Figure 12.5, you can see that the curve is traced as t increases
from -2 to 2.
21
24
24
24
6
Parabolic cylinder
(0, 0, 2)
C: x=1
y=r
(6 +124-1)
6
Ellipsoid
Curve in
space
(-2,4,0)
(2, 4,0)
The curve C is the intersection of the semiellipsoid and the parabolic cylinder.
Figure 12.5

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Tags:
ellipsoid

parabola

parabolic cylinder

Space curve

Trace vector

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