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formuls for final

# formuls for final - 3 2 3 2 n a x a f a x a f a x a f a x a...

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Known Series ... 1 1 1 4 3 2 + + + + + = - x x x x x ... 4 3 2 1 ) 1 ( 1 3 2 2 + + + + = - x x x x ... 4 3 2 ) 1 ln( 4 3 2 + - + - = + x x x x x ... ! 4 ! 3 ! 2 1 4 3 2 + + + + + = x x x x e x ... ! 7 ! 5 ! 3 sin 7 5 3 + - + - = x x x x x ... ! 6 ! 4 ! 2 1 cos 6 4 2 + - + - = x x x x ... ! 7 ! 5 ! 3 sinh 7 5 3 + + + + = x x x x x ... ! 6 ! 4 ! 2 1 cosh 6 4 2 + + + + = x x x x ... 7 5 3 tan 7 5 3 1 + - + - = - x x x x x ( 29 ... 3 2 1 1 1 3 2 + + + + = + x p x p x p x p Other Formulas Volume (disks) = b a dx x f V ) ( 2 π (shells) = b a dx x xf V ) ( 2 π dx dx dy ds 2 1 + = or dt dt dy dt dx ds 2 2 + = length b a ds surface area b a ds x f ) ( 2 π [ ] [ ] - - = b a b a dx x g x f dx x g x f x x ) ( ) ( ) ( ) ( [ ] [ ] - - = b a b a dx x g x f dx x g x f y ) ( ) ( ) ( ) ( 2 1 2 2 + = - - C a u u a du 1 2 2 sin Trapezoidal method [ ] ) ( ) ( 2 ... ) ( 2 ) ( 2 ) ( 1 1 0 n n b a x f x f x f x f h dx x f + + + + - where n a b h - = Parabolic method [ ] ) ( ) ( 4 ... ) ( 2 ) ( 4 ) ( 3 ) ( 1 2 1 0 n n b a x f x f x f x f x f h dx x f + + + + + - Taylor Polynomial
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Unformatted text preview: ! ) )( ( ... ! 3 ) )( ( ' ' ' ! 2 ) )( ( ' ' ) )( ( ' ) ( ) ( ) ( 3 2 n a x a f a x a f a x a f a x a f a f x f n n-+ +-+-+-+ ≈ Maclaurin Polynomial ! ) ( ... ! 3 ) ( ' ' ' ! 2 ) ( ' ' ) ( ' ) ( ) ( ) ( 3 2 n x f x f x f x f f x f n n + + + + + ≈ Newton’s method ) ( ' ) ( 1 n n n n x f x f x x-= +...
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