2.1 - 3D Graphs - Multivariable Calculus

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Last updated 2:02 PM on 9/21/26
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18 Terms

1
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z = Ax² + By²

Elliptic paraboloid

<p>Elliptic paraboloid</p>
2
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<p>Level curves for elliptic paraboloid </p>

Level curves for elliptic paraboloid

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3
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<p>Vertical section for elliptic paraboloid </p>

Vertical section for elliptic paraboloid


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4
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z = Ax² + By² except A and B have opposite signs (so more like Ax² - By²

Hyperbolic paraboloid

<p>Hyperbolic paraboloid </p>
5
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<p>Level curves for hyperbolic paraboloid </p>

Level curves for hyperbolic paraboloid

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6
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<p>Vertical sections for hyperbolic paraboloid</p>

Vertical sections for hyperbolic paraboloid

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7
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x²/A² + y²/B² + z²/C² = 1

Ellipsoid

<p>Ellipsoid</p>
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<p>Ellipsoid level curves</p>

Ellipsoid level curves

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9
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<p>Ellipsoid vertical sections</p>

Ellipsoid vertical sections

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10
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z² = Ax² + By²

Double cone

<p>Double cone</p>
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<p>Double cone level curve</p>

Double cone level curve

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12
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<p>Double cone vertical sections </p>

Double cone vertical sections

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13
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x²/A² + y²/B² - z²/C² = 1

Hyperboloid if one sheet

<p>Hyperboloid if one sheet</p>
14
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<p>Hyperboloid of one sheet level curves </p>

Hyperboloid of one sheet level curves

Imagine it when setting one variable = 0

<p>Imagine it when setting one variable = 0</p>
15
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<p>Hyperboloid of one sheet vertical sections</p>

Hyperboloid of one sheet vertical sections

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16
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-x²/A² - y²/B² + z²/C² = 1

Hyperboloid of two sheets

<p>Hyperboloid of two sheets</p>
17
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<p>Hyperboloid of two sheets level curves </p>

Hyperboloid of two sheets level curves

Imagine them when setting one variable = 0

<p>Imagine them when setting one variable = 0</p>
18
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<p>Hyperboloid of two sheets vertical sections </p>

Hyperboloid of two sheets vertical sections

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