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2
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1 − cos x x = 0, x2 1 − cos x = O x 2 , ( ) x → 0. 1 − cos x 1 + cos x 2 , x ≥ε ≥ ≥ 2, x 2 x 2 ε x∈ R \ { x < ε} 1 − cos x x2 , 1 − cos x = O x 2 ( ) x ∈ R \ {0} . 3. f (x ) f (x) g ( x) x →a, lim = 0. x→a g (x ) f ( x ) = o ( g ( x )) , x→a. 1 1 − − e x2 e x2 = t → 0, x → 0, t lim = = lim ; 3. x→0 x 1 t→ 0 1 x= . − ln t − ln t 1 ′ − t 2 − ln t − (ln t ) t t2 lim = lim = lim = lim = lim = 0, t→0 1 t→0 1 t→0 ′ t→0 − 2 t →0 2 1 − ln t t2 2 t3 t 1 − x2 1 e − lim x→ 0 =0 e x2 = o( x ) , x → 0. x . a 1, 2, 3 , , x , , . . 4. , ψ 0 ( x ),ψ 1 ( x ),ψ 2 (x ),...,ψ n (x ),.... , n = 0,1, 2, .... ψ n+1 ( x ) = (ψ n ( x )) , x → ∞.