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14.1.1-240926 Level Sets
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Expression 10: "f" left parenthesis, "x" , "y" , right parenthesis left brace, "z" equals 2.9 9 9 , right brace
f
x
,
y
z
=
2
.
9
9
9
10
(3) Plot the level curves for values of c from 0 to 3, increasing in increments of 0.5. (give desmos some time for this)
(3) Plot the level curves for values of c from 0 to 3, increasing in increments of 0.5. (give desmos some time for this)
11
Expression 12: "f" left parenthesis, "x" , "y" , right parenthesis left brace, "z" equals "I" , right brace
f
x
,
y
z
=
I
12
(4) Imagine drawing a level curve of value c for EVERY 0<c<3. What would we get?
(4) Imagine drawing a level curve of value c for EVERY 0<c<3. What would we get?
13
(5) Imagine raising a level urve of value c into 3D up to the plane z=c.
(5) Imagine raising a level urve of value c into 3D up to the plane z=c.
14
To see what we get, rotate the "xy-plane" into the "xyz-space.
To see what we get, rotate the "xy-plane" into the "xyz-space.
15
Hit the wrench icon (upper right) and select "Translucent Surfaces".
Hit the wrench icon (upper right) and select "Translucent Surfaces".
16
Next hit the dot below to graph the z=f (x,y).
Next hit the dot below to graph the z=f (x,y).
17
Expression 18: "f" left parenthesis, "x" , "y" , right parenthesis equals StartRoot, 9 minus "x" squared minus "y" squared , EndRoot
f
x
,
y
=
9
−
x
2
−
y
2
18
All Done .
All Done .
19
Ignore this set-up folder (colors)
Ignore this set-up folder (colors)
Hide this folder from students.
20
27
powered by
powered by
"x"
x
"y"
y
"z"
z
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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