Activity 9.1.6. In the following questions, we investigate the use of traces to better understand a function through both tables and graphs. a. Identify the y = 0.6 trace for the distance function f defined by f(x, y)=sin(2) by highlighting or circling the appropriate cells in Table 9.1.5. Write a sentence to describe the behavior of the function along this trace. Table 9.1.5. Values of f(x, y) = ²(2) 9 z\y 0.2 0.4 0.6 0.8 1.0 18.2 19.5 17.8 13.2 25 7.6 14.0 56.0 50 30.4 72.8 78.1 71.0 75 68.4 163.8 175.7 159.8 100 121.7 224.2 291.3 312.4 284.2 125 190.1 350.3 455.1 444.0 329.8 163.6 150 273.8 504.4 655.3 702.8 639.3 474.9 235.5 175 372.7 686.5 892.0 956.6 870.2 646.4 200 486.8 896.7 1165.0 1249.5 1136.6 844.3 418.7 225 616.2 1134.9 1474.5 1581.4 1438.5 1068.6 530.0 250 760.6 1401.1 1952.3 1776.0 1319.3 654.3 1.2 1.4 6.5 26.2 118.7 58.9 211.1 104.7 in-context b. Identify the x = 150 trace for the distance function by highlighting or circling the appropriate cells in Table 9.1.5. Write a sentence to describe the behavior of the function along this trace. Figure 9.1.13. Coordinate axes to sketch traces. c. For the function g defined by g(x, y) = x² + y² +1, explain the type of function that each trace in the direction will be (keeping y constant). Plot the y = -4, y = -2, y = 0, y = 2, and y = 4 traces in 3-dimensional coordinate system provided in Figure 9.1.13. d. For the function g defined by g(x, y) = x² + y2 +1, explain the type of function that each trace in the y direction will be (keeping a constant). Plot the z = -4, z = -2, z = 0, z = 2, and z = 4 traces in 3-dimensional coordinate system in Figure 9.1.13. e. Describe the surface generated by the function g.
Activity 9.1.6. In the following questions, we investigate the use of traces to better understand a function through both tables and graphs. a. Identify the y = 0.6 trace for the distance function f defined by f(x, y)=sin(2) by highlighting or circling the appropriate cells in Table 9.1.5. Write a sentence to describe the behavior of the function along this trace. Table 9.1.5. Values of f(x, y) = ²(2) 9 z\y 0.2 0.4 0.6 0.8 1.0 18.2 19.5 17.8 13.2 25 7.6 14.0 56.0 50 30.4 72.8 78.1 71.0 75 68.4 163.8 175.7 159.8 100 121.7 224.2 291.3 312.4 284.2 125 190.1 350.3 455.1 444.0 329.8 163.6 150 273.8 504.4 655.3 702.8 639.3 474.9 235.5 175 372.7 686.5 892.0 956.6 870.2 646.4 200 486.8 896.7 1165.0 1249.5 1136.6 844.3 418.7 225 616.2 1134.9 1474.5 1581.4 1438.5 1068.6 530.0 250 760.6 1401.1 1952.3 1776.0 1319.3 654.3 1.2 1.4 6.5 26.2 118.7 58.9 211.1 104.7 in-context b. Identify the x = 150 trace for the distance function by highlighting or circling the appropriate cells in Table 9.1.5. Write a sentence to describe the behavior of the function along this trace. Figure 9.1.13. Coordinate axes to sketch traces. c. For the function g defined by g(x, y) = x² + y² +1, explain the type of function that each trace in the direction will be (keeping y constant). Plot the y = -4, y = -2, y = 0, y = 2, and y = 4 traces in 3-dimensional coordinate system provided in Figure 9.1.13. d. For the function g defined by g(x, y) = x² + y2 +1, explain the type of function that each trace in the y direction will be (keeping a constant). Plot the z = -4, z = -2, z = 0, z = 2, and z = 4 traces in 3-dimensional coordinate system in Figure 9.1.13. e. Describe the surface generated by the function g.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Activity 9.1.6
Transcribed Image Text:Activity 9.1.6. In the following questions, we investigate the use of traces to
better understand a function through both tables and graphs.
a. Identify the y = 0.6 trace for the distance function f defined by
f(x, y)=sin(2y) by highlighting or circling the appropriate cells in
9
Table 9.1.5. Write a sentence to describe the behavior of the function
along this trace.
Table 9.1.5. Values of f(x, y) =
\y 0.2
25
0.4
7.6 14.0
50 30.4 56.0
0.6
18.2
72.8
163.8
291.3
125 190.1 350.3 455.1
150 273.8 504.4
655.3
702.8
175 372.7 686.5
892.0 956.6
200 486.8 896.7 1165.0 1249.5 1136.6
844.3 418.7
225 616.2 1134.9 1474.5 1581.4 1438.5 1068.6 530.0
250 760.6 1401.1
1952.3 1776.0 1319.3 654.3
75 68.4
100 121.7 224.2
I
z²sin(2y)
9
4
0.8
1.0
19.5
17.8
78.1 71.0
-2
b. Identify the x = 150 trace for the distance function by highlighting or
circling the appropriate cells in Table 9.1.5. Write a sentence to describe
the behavior of the function along this trace.
175.7 159.8 118.7
312.4
284.2
444.0
639.3
870.2 646.4
1.2 1.4
13.2
6.5
26.2
58.9
211.1 104.7
329.8 163.6
474.9 235.5
2
2
4
in-context
Y
Figure 9.1.13. Coordinate axes to sketch traces.
c. For the function g defined by g(x, y) = x² + y² + 1, explain the type of
function that each trace in the a direction will be (keeping y constant).
Plot the y = -4, y = -2, y = 0, y = 2, and y = 4 traces in 3-dimensional
coordinate system provided in Figure 9.1.13.
d. For the function g defined by g(x, y) = x² + y² + 1, explain the type of
function that each trace in the y direction will be (keeping a constant).
Plot the x = -4, z = -2, x=0, x=2, and x = 4 traces in 3-dimensional
coordinate system in Figure 9.1.13.
e. Describe the surface generated by the function g.
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