# Calc III Exam II Prep

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(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1

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### 13 Terms

1

(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1

Ellipsoid (All traces are ellipses)

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2

z=(x^2/a^2)+(y^2/b^2)

Elliptic Paraboloid (Made of ellipses and parabolas)

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3

(x^2/a^2)+(y^2/b^2)-(z^2/c^2)=1

Hyperboloid of one sheet (connected)

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4

(-x^2/a^2)-(y^2/b^2)+(z^2/c^2)=1

Hyperboloid of two sheets (disconnected)

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5

(x^2/a^2)+(y^2/b^2)=(z^2/c^2)

Elliptic Cone (Two inverted cones touching tips)

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6

(x^2/a^2)-(y^2/b^2)=z

Hyperbolic paraboloid (Two hyperbolas connected)

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7

x to spherical

x = ρ cosθ sinφ

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8

y to spherical

x = ρ sinθ sinφ

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9

z to spherical

x = ρ cosφ

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10

ρ^2 = ?

ρ^2 = x^2 + y^2 + z^2

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11

Spherical integral

∫∫∫ p^2sinφdφdρdθ

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12

Linear Approximation

L(x,y) = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b)

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13

Average Value

(1/b-a)(1/d-c) ∫∫f(x,y)dydx (from a to b and from c to d)

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