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Консультация № 118518
15.01.2008, 05:22
0.00 руб.
0
2
2
Уважаемые эксперты, помогите, пожалуйста, решить задачу:
lim (x^3-3x^2+4)/(x^4-4x^2)
x->2
Спасибо за рассмотрение.
Приложение:
x->2 -x стремится к двум
lim (x^3-3x^2+4)/(x^4-4x^2)
x->2
Спасибо за рассмотрение.
Приложение:
x->2 -x стремится к двум
Обсуждение
Неизвестный
15.01.2008, 13:22
общий
это ответ
Здравствуйте, Котова Даша!
Т.к. x³-3x²+4=(x+1)·(x-2)², а x^4-4x²=x²·(x²-4), то
при x->2
lim(x³-3x²+4)/(x^4-4x²)=lim(x+1)·(x-2)·(x-2)/(x²·(x-2)·(x+2))=lim(x+1)·(x-2)/(x²·(x+2))=0
Ответ: 0.
Приложение:
lim(x³-3x²+4)/(x^4-4x²)=x->2=lim(x+1)·(x-2)·(x-2)/(x²·(x-2)·(x+2))= x->2=lim(x+1)·(x-2)/(x²·(x+2))=0 x->2
Т.к. x³-3x²+4=(x+1)·(x-2)², а x^4-4x²=x²·(x²-4), то
при x->2
lim(x³-3x²+4)/(x^4-4x²)=lim(x+1)·(x-2)·(x-2)/(x²·(x-2)·(x+2))=lim(x+1)·(x-2)/(x²·(x+2))=0
Ответ: 0.
Приложение:
lim(x³-3x²+4)/(x^4-4x²)=x->2=lim(x+1)·(x-2)·(x-2)/(x²·(x-2)·(x+2))= x->2=lim(x+1)·(x-2)/(x²·(x+2))=0 x->2
Неизвестный
17.01.2008, 19:28
общий
это ответ
Здравствуйте, Котова Даша!
lim (x^3-3x^2+4)/(x^4-4x^2)
x->2
Числитель (x^3-3x^2+4) разложим на множители (x-2)^2(x+1) делением в столбик на (x-2) два раза.
Знаменатель (x^4-4x^2) тоже разложим на множители x^2(x+2)(x-2).
Теперь наш придел имеет вид
lim (x-2)^2(x+1)/ x^2(x+2)(x-2)
x->2
Сократим дробь под знаком предела на x-2
lim (x-2)(x+1)/ x^2(x+2)
x->2
Числитель стремится к 0, а знаменатель - к 16, поэтому предел равен 0.
lim (x^3-3x^2+4)/(x^4-4x^2)
x->2
Числитель (x^3-3x^2+4) разложим на множители (x-2)^2(x+1) делением в столбик на (x-2) два раза.
Знаменатель (x^4-4x^2) тоже разложим на множители x^2(x+2)(x-2).
Теперь наш придел имеет вид
lim (x-2)^2(x+1)/ x^2(x+2)(x-2)
x->2
Сократим дробь под знаком предела на x-2
lim (x-2)(x+1)/ x^2(x+2)
x->2
Числитель стремится к 0, а знаменатель - к 16, поэтому предел равен 0.
Форма ответа
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