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The Russian Healthcare System

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Таблица эквивалентных б.м х->0 sin х ~ x tg x ~ x arcsin x ~ x arctg x ~ x 1 – cos x ~ x2 /2 ln(1+x) ~ x loga (1+x) ~ x/lna ex – 1 ~ x ax – 1 ~ x • lna (1+x)p – 1 ~ px

Таблица эквивалентных б.м х -> a ; ά(x) ->0

sin ά(x) ~ ά(x) tg ά(x) ~ ά(x) arcsin ά(x) ~ ά(x) arctg ά(x) ~ ά(x) 1 – cos ά(x)~ (ά(x) )2 /2 ln(1+ ά(x)) ~ ά(x) loga (1+ ά(x)) ~ ά(x) /lna eά(x) – 1 ~ ά(x) aά(x) – 1 ~ ά(x) • lna (1+ ά(x))p – 1 ~ p ά(x) | |
|(a+b)2=a2+2ab+b2 |
|(a-b)2=a2-2ab+b2 |
|a2-b2=(a-b)(a+b) |
| |
|(a+b)3=a3+3a2b+3ab2+b3 |
|(a-b)3=a3-3a2b+3ab2-b3 |
|a3+b3=(a+b)(a2-ab+b2) |
|a3-b3=(a-b)(a2+ab+b2) |

| |
|1ый замечательный предел: |
|lim sin x = 1 |
|X ->0 X |
|lim f(x) = b => lim g(x) = |
|1 |
|x ->a g(x) x ->a |
|f(x) b |
|Следствие: |
|lim tg x = 1 |
|X ->0 X |
|lim arcsin x = 1 |
|X ->0 X |
|lim arctg x = 1 |
|X ->0 X |
|lim 1- cos x = 1 |
|X ->0 (x2/2) |

| |
| |
|2ой замечательный предел: |
|lim (1+x)1/x = e |
|X ->0 |
|Следствие: |
|lim loga (1+ x) = 1 |
|X ->0 X |
|lim loga (1+ x) = 1 |
|X ->0 x/lna |
|lim ex - 1 = 1 |
|X ->0 X |
|lim ax - 1 = 1 |
|X ->0 x · ln |
|lim (1+x)p - 1 = 1 |
|X ->0 P • X |

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