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Задать вопрос экспертам

Консультация № 149357

03.11.2008, 07:57

0.00 руб.

03.11.2008, 07:58

0 1 1

Образование

У меня возникла проблема с решением нескольких задач:
1) Составить уравнение касательной и нормаль к графику функции y=f(x) в точке Мо(xo;yo), соответствующей значениям х=хо, y=f(xo). Указать касательный и нормальный векторы к графику функции в точке Мо. y=(x/(x+2)), хо=2

2) Вычислить площадь фигуры, ограниченной линиями (площадь области D)

http://cs1581.vkontakte.ru/u3532226/50322035/x_0608cfc6.jpg

Обсуждение

Неизвестный

04.11.2008, 17:16

общий

это ответ

Здравствуйте, Darklily!
1 задача:
т.к. х0 =2; f(х0)=2/(2+2) = 2/4 = 1/2; f ’(х)= (x+2-x)/(x+2)² = 2/(x+2)² ; f ’(х0)=2/(2+2)²=2/16=1/8, то
уравнение касательной y= f ’(х0)•(x-x0) + f (х0) принимает вид:
y=1/8 • (x - 2) + 1/2;
y=x/8 + 1/4

уравнение нормали y= {-1/f ’(х0)}•(x-x0) + f (х0) принимает вид:
y=–8 • (x - 2) + 1/2;
y=–8x + 16 ½

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