Question

Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) x = y^2 + 7z^2 (Write an equation for the cross section at z = 0 using x and y.) x = y^2 (Write an equation for the cross section at y = 0 using x and z.) x = 7z^2 (Write an equation for the cross section at x = -7 using y and z.) 1 = -y^2/7 + z^2 (Write an equation for the cross section at x = 0 using y and z.) 0 = y^2 + 7z^2 (Write an equation for the cross section at x = 7 using y and z.) 1 = y^2/7 + z^2

          Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
x = y^2 + 7z^2
(Write an equation for the cross section at z = 0 using x and y.)
x = y^2
(Write an equation for the cross section at y = 0 using x and z.)
x = 7z^2
(Write an equation for the cross section at x = -7 using y and z.)
1 = -y^2/7 + z^2
(Write an equation for the cross section at x = 0 using y and z.)
0 = y^2 + 7z^2
(Write an equation for the cross section at x = 7 using y and z.)
1 = y^2/7 + z^2

Show more…

Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
x = y^2 + 7z^2
(Write an equation for the cross section at z = 0 using x and y.)
x = y^2
(Write an equation for the cross section at y = 0 using x and z.)
x = 7z^2
(Write an equation for the cross section at x = -7 using y and z.)
1 = -y^2/7 + z^2
(Write an equation for the cross section at x = 0 using y and z.)
0 = y^2 + 7z^2
(Write an equation for the cross section at x = 7 using y and z.)
1 = y^2/7 + z^2

Added by Alexander J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/22/2023

Step 1

) y=-7x+15 Show more…

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Use traces to sketch the surface. (If an answer does not exist, enter DNE.) Select "Update Graph" to see your response plotted on the screen. Select the "Submit" button to grade your response. x = y^2 + 7z^2 (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at y = 0 using x and z.) x = 7z^2 (Write an equation for the cross section at x = 7 using y and z.) (Write an equation for the cross section at x = 0 using y and z.) (Write an equation for the cross section at x = 7 using y and z.)

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Transcript

00:01 Hello everyone, welcome to this video.

00:04 So, here we are given with the equation and we have to find the trace.

00:08 So, let us find one by one.

00:10 So, here we have to find when it is x y trace.

00:15 So, z is equal to 0.

00:18 So, by putting z is equal to 0, we get x is equal to y square.

00:24 So, this equation resembles parabola.

00:32 So, therefore, this graph on x y trace will be a parabola which goes like this.

00:46 So, here it is parabola at x is equal to y square.

00:52 Considering the next one, x is a trace y equal to 0.

00:57 If we put y is equal to 0, we get that is 7 z square.

01:06 So, when y is equal to 0, we get x is equal to 7 z square.

01:17 So, here this equation also resembles parabola.

01:25 So, here the graph will be similarly to this that is it goes like this.

01:37 So, it will be at x is a trace when x is equal to 7 z square.

01:44 Here next we have at x is equal to minus 7, let us find.

01:54 So, you are taking x is equal to minus 7, we get y square plus 7 z square.

02:00 So, we get on dividing the whole term by 7, we get minus 1 equal to y square by 7 plus z square.

02:12 So, here it is not possible because squaring two terms will not give minus 1.

02:19 So, this is never possible.

02:21 So, this case is not possible to trace.

02:24 And at x is equal to 0, the value will be y square 0 equal to y square plus 7 z square.

02:34 So, we can consider this is minus y square equal to 7 z square.

02:38 So, this also is possible only if y is z is equal to 0...

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