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Консультация № 201412
20.09.2021, 10:53
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Составить уравнение нормали к данной кривой в точке с абсциссой x0
у=(4х-х^2)/4, x0=2
Составить уравнение нормали к данной кривой в точке с абсциссой x0
у=(4х-х^2)/4, x0=2
Обсуждение
20.09.2021, 13:21
общий
Сразу найдем уравнение касательной, взяв производную:
y =(4-2x)/4 = 1-0,5x,
т. е угловой коэффициент этой прямой равен = -0,5.
Следовательно, угловой коэффициент нормали есть = 2,
т. к. произведение угловых коэффициентов взаимно перпендикулярных прямых = -1.
Итак, уравнение нормали^
y = 2x + b, подставив значения х0=2, y0=0,
найдем b = -4,
y = 2x - 4
y =(4-2x)/4 = 1-0,5x,
т. е угловой коэффициент этой прямой равен = -0,5.
Следовательно, угловой коэффициент нормали есть = 2,
т. к. произведение угловых коэффициентов взаимно перпендикулярных прямых = -1.
Итак, уравнение нормали^
y = 2x + b, подставив значения х0=2, y0=0,
найдем b = -4,
y = 2x - 4
Форма ответа
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