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BasicMath

BasicMath - Basic Mathematical Relations 1 e = lim1 2.718 n...

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Basic Mathematical Relations e = n n n + 1 1 lim 2.718 Log and power L L xy y x ln ln ln = + + , y x y x ln ln ln = , a x x a ln ln = a b b c c a log log log = , x x 10 log log = , x x e log ln = z y x z y x a a a a + + = , y x y x a a a = / , ( ) xy y x a a = Derivatives dg df g f d + = + ) ( , gdf fdg fg d + = ) ( 2 g fdg gdf g f d = dx x dg x dg x g df dx x g df ) ( ) ( )) ( ( )) ( ( = 1 = n n nx dx dx (for 0 n ) , ax ax ae dx de = , x dx x d 1 ln = Integrals + + = + const n x dx x n n 1 1 , const x dx x + = ln 1 , const e a dx e ax ax + = 1 Sum and multiplication = + + + = n i i a a a a 1 3 2 1 L , = = n i i a a a a 1 3 2 1 L Taylor expansions ( ) = = = 0 ! 1 ) ( n n a x n n a x dx f d n x f , L + + + = 2 2 1 1 x x e x
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