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Миронычев Виталий: Пока 3й вопрос не видно, выкладываю сюда. 1.(1-sin3x)/cos2x=(1-sin3x)/(1-sin2x)=(1+sinx+sin2x)/(1+sinx) limx->π/2(1+sinx+sin2x)/(1+sinx)=(1+1+1)/(1+1)=3/2
Roman Chaplinsky / Химик CH: Добрый день! Непонятен 3й предел lim(cosx+3sinx), дальше неразборчиво. Что посоветуете делать: ждать, пока исправит, или давать ответ на два? С уважением.
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10.10.2010, 12:16
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lamed: Абсолютно согласен с вами-что 3-ий предел не совсем ясно За это приношу извинения lim(cosx+sin3x) ^1/2x (при x->0)
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10.10.2010, 12:16
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Roman Chaplinsky / Химик CH: прошу прощения за пример-вот разяснение lim(cosx+sin3x) ^1/2x (при x->0)
Используя I замечательный предел, получим, 2*((2x/x)*(2x/9x)+(3.5x/x)*(3.5x/9x))=2*(2*2+3,5*3,5)/(1*9)=2*16,25/9=32,5/9=65/18
3. limx->0 (cosx+3sinx)1/2x Последовательно используем I замечательный предел, свойство бесконечно малых более высокого порядка малости, II замечательный предел. cosx+sin3x=1-2*sin2(x/2)+sin3x=1-2(x/2)2+3x=1+3x ( так как при x->0, x2<<x )
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Решение MathCAD-7. С уважением.
