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¢ ----- n 9 0 0 0 1 0 1 1 0 1 lim 0 n n n m m x m a n m b a x a x a n m b x b x b n m - - →∞ = + + + = < + + + L L À Ir 0 0 0 0 0 10 0 sin lim 1 x x x = 20 ( 29 1 0 lim 1 x x x e + = 30 lim ( ) 1 n n a a o →∞ = 40 lim 1 n n n →∞ = * 50 limarctan 2 x x π →∞ = * 60 lim tan 2 x arc x π →-∞ = - 70 limarccot 0 x x →∞ = 80 lim arccot x x π →-∞ = 90 lim 0 x x e →-∞ = 100 lim x x e →+∞ = ∞ & 110 0 lim 1 x x x + = ¸y & 0 x sin x x : tan x x : arcsin x x : arctan x x : 2 1 1 cos 2 x x - : []=- ( 29 ln 1 x x + : 1 x e x - : 1 ln x a x a - : ( 29 1 1 x x + - : : ° ( ( 29 u v u v ± = ± ( 29 uv u v uv = + 2 u u v uv v v - = ( 29 0 c = 1 x x μ μ μ - = ( 29 sin cos x x = ( 29 cos sin x x = - ( 29 2 tan sec x x = ( 29 2 cot csc x x = - ( 29 sec sec tan x x x = ( 29 csc csc cot x x x = - 1
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l ----- 0 ( 29 x x e e = ( 29 ln x x a a a = ( 29 1 ln x x = ( 29 1 log ln x a x a = ( 29 2 1 arcsin 1 x x = - ( 29 2 1 arccos 1 x x = - - ( 29 2 1 arctan 1 x x = + ( 29 2 1 arccot 1 x x = - + ( 29 1 x = ( 29 1 2 x x = 10 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 n n n u x v x u x v x ± = ± 20 ( 29 ( 29 ( 29 ( 29 n n cu x cu x = 30 ( 29 ( 29 ( 29 ( 29 n n n u ax b a u ax b + = + 40 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( ) 0 n n n k k k n k u x v x c u x v x - = = ¬ n ¬ 1 10 ( 29 ( 29 !
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