Calc 3 Graphs + Important info

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Last updated 4:17 PM on 10/8/26
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14 Terms

1
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x²+y²=R

Sphere

<p>Sphere</p>
2
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x²+y²=9

Cylinder → Missing var extends along that axis

<p>Cylinder → Missing var extends along that axis</p>
3
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x²/a² + y²/b² + z²/c² = 1

Ellipsoid

<p>Ellipsoid</p>
4
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z = Ax² +By²

Elliptic paraboloid → linear var tells direction of “bowl” opening

<p>Elliptic paraboloid → linear var tells direction of “bowl” opening </p>
5
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z = Ay² - Bx²

Hyperbolic paraboloid (saddle)

<p>Hyperbolic paraboloid (saddle) </p>
6
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z² = x² + y²

Cone

<p>Cone</p>
7
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u • v = (Geometric def)

|u| |v| cosθ

8
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Area parallelogram given 2 vectors

|u x v| =|u| |v| sinθ

9
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Area of triangle

= ½ |u x v|

10
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u • v = 0

Vectors are Perpendicular

11
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u x v = 0

Vectors are Parallel

12
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u • v > 0

Angle between vectors is acute

13
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u • v < 0

Angle between vectors is Obtuse

14
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To find tangent lines given to=

= (Point @ to)+ v(to)s