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Консультация № 166631
06.05.2009, 17:42
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Здравствуйте уважаемые эксперты! помогите, пожалуйста с таким примером:
Функция f(x) представляет собой сумму трёх одночленов. Указать среди них одночлен, эквивалентный всей сумме: а)при x →0 б)x →бескон.
f(x)=-2x^2+4x-3корень 4 степени из x^3
Функция f(x) представляет собой сумму трёх одночленов. Указать среди них одночлен, эквивалентный всей сумме: а)при x →0 б)x →бескон.
f(x)=-2x^2+4x-3корень 4 степени из x^3
Обсуждение
Неизвестный
06.05.2009, 18:30
общий
это ответ
Здравствуйте, Кузьминов В.В.!
Если я правильно понял, то речь идет о функции f(x)=-2x^2+4x-3*x^(3/4).
Если функции f(x) и g(x) эквивалентны, то lim{x→a}(f(x)/g(x)) = 1.
а) Для поиска эквивалентного одночлена при x→0 возьмем одночлен наименьшей степени, т.е. (-3*x^(3/4)). Докажем, что он - то, что нужно
lim{x→0}(-2x^2+4x-3*x^(3/4))/(-3*x^(3/4))= lim{x→0}((2/3)*x^(5/4)-(4/3)*x^(1/4)+1)=0-0+1=1.
б) Для поиска эквивалентного одночлена при x→0 возьмем одночлен наибольшей степени, т.е. (-2x^2). Докажем, что он - то, что нужно
lim{x→∞}(-2x^2+4x-3*x^(3/4))/(-2x^2)= lim{x→∞}(1-2/x+(3/2)/x^(5/4))=1-0+0=1.
Ответ: а) (-3*x^(3/4)), б) (-2x^2)
Если я правильно понял, то речь идет о функции f(x)=-2x^2+4x-3*x^(3/4).
Если функции f(x) и g(x) эквивалентны, то lim{x→a}(f(x)/g(x)) = 1.
а) Для поиска эквивалентного одночлена при x→0 возьмем одночлен наименьшей степени, т.е. (-3*x^(3/4)). Докажем, что он - то, что нужно
lim{x→0}(-2x^2+4x-3*x^(3/4))/(-3*x^(3/4))= lim{x→0}((2/3)*x^(5/4)-(4/3)*x^(1/4)+1)=0-0+1=1.
б) Для поиска эквивалентного одночлена при x→0 возьмем одночлен наибольшей степени, т.е. (-2x^2). Докажем, что он - то, что нужно
lim{x→∞}(-2x^2+4x-3*x^(3/4))/(-2x^2)= lim{x→∞}(1-2/x+(3/2)/x^(5/4))=1-0+0=1.
Ответ: а) (-3*x^(3/4)), б) (-2x^2)
09.06.2020, 07:52
общий
Адресаты:
Функция f(x)=x^4+3x-3cos2x представляет собой сумму одночленов. Указать среди них одночлен, эквивалентный функции f(x) : а) при x→0 ; б) при x→00
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