MATH114 Fall 2007 - Final Cheat Sheet

MATH114 Fall 2007 - Final Cheat Sheet - 13.5 Equations of...

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Unformatted text preview: 13.5 Equations of Lines and Planes Distance from a point to a plane: 1 1 1 2 2 2 ax by cz d D a b c + + + = + + 13.7 Cylindrical and Spherical Coordinates Rectangular ( , , ) x y z Cylindrical ( , , ) r z 2 2 2 r x y = + , tan x y = , z = z Cylindrical ( , , ) r z Rectangular ( , , ) x y z cos x r = , sin y r = , z z = Rectangular ( , , ) x y z Spherical ( , , ) 2 2 2 2 x y z = + + , cos z = , cos sin x = Spherical ( , , ) Rectangular ( , , ) x y z sin cos x = , sin sin y = , cos z = Spherical ( , , ) Cylindrical ( , , ) r z sin r = , = , cos z = 14.3 Arc Length and Curvature Arc Length : [ ] [ ] [ ] 2 2 2 '( ) '( ) '( ) '( ) b b a a L f t g t h t dt r t dt = + + = Arc Length Function : ( ) '( ) t a s t r u du = , length of curve from a to t. Curvature : 3 '( ) '( ) ''( ) '( ) '( ) T t r t r t dT ds r t r t = = = Normal and Binormal Vectors: '( ) ( ) '( ) T t N t T t = , ( ) ( ) ( ) B t N t T t = Plane with T and N = Osculating Plane...
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This note was uploaded on 04/17/2008 for the course MATH 114 taught by Professor Temkin during the Fall '07 term at UPenn.

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MATH114 Fall 2007 - Final Cheat Sheet - 13.5 Equations of...

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