Так как это куб, то диагонали каждой грани - диагонали квадрата, угол = 90
(x-2)(x-3 1/3)=0
x-2=0 или x-3 1/3=0
При x=1 или x=2
8х³ - у³ = (2х - у)(4х² + 2ху + у²) = 3(4х² - 4ху + у² + 6ху) = 3((2х - у)² + 6ху) = 3(3² - 12) = 3(9 - 12) = 3•(-3) = -9.
∫(dx/(x²+x-6))=∫dx/(x²+2*x*(1/2)+1/4-1/4-6)=∫(dx/((x+1/2)²-25/4)=
=∫(dx/(-(5/2)²-(x+1/2)²).
Используем формулу "Высокого логарифма":
∫(dx/(a²-x²)=(1/(2a))*(ln|a+x|/ln|a-x|)+C x≠a
(1/(2*5/2))*(ln|(-5/2+x+1/2)|/ln|(-5/2-x-1/2|)=
=(ln|x-2|/ln|-x-3|)/5==(ln|x-2|/ln|-(x+3)|)/5=(ln|x-2|/ln|x+3|)/5.
![0,23=0,22999.....=0,22+9 \frac{1}{1000}+9 \frac{1}{10000} +...=\\ =0,22+9( \frac{1}{1000}+ \frac{1}{10000}+...)](https://tex.z-dn.net/?f=0%2C23%3D0%2C22999.....%3D0%2C22%2B9+%5Cfrac%7B1%7D%7B1000%7D%2B9+%5Cfrac%7B1%7D%7B10000%7D++%2B...%3D%5C%5C%0A%3D0%2C22%2B9%28+%5Cfrac%7B1%7D%7B1000%7D%2B+%5Cfrac%7B1%7D%7B10000%7D%2B...%29)
Считаем сумму ряда
![\frac{1}{1000}+ \frac{1}{10000} +...= \frac{ \frac{1}{1000} }{1- \frac{1}{10} } = \frac{1}{900}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B1000%7D%2B+%5Cfrac%7B1%7D%7B10000%7D++%2B...%3D+%5Cfrac%7B+%5Cfrac%7B1%7D%7B1000%7D+%7D%7B1-+%5Cfrac%7B1%7D%7B10%7D+%7D+%3D+%5Cfrac%7B1%7D%7B900%7D+)
Получаем:
![0,22+9 \frac{1}{900} =0,22+ \frac{1}{100}](https://tex.z-dn.net/?f=0%2C22%2B9+%5Cfrac%7B1%7D%7B900%7D+%3D0%2C22%2B+%5Cfrac%7B1%7D%7B100%7D+)
![0,22=0+ \frac{22}{100}=>0,22+ \frac{1}{100}= \frac{23}{100}](https://tex.z-dn.net/?f=0%2C22%3D0%2B+%5Cfrac%7B22%7D%7B100%7D%3D%3E0%2C22%2B+%5Cfrac%7B1%7D%7B100%7D%3D+%5Cfrac%7B23%7D%7B100%7D+++)
Второе выражение:
![0,15=0,14999....=0,14+9( \frac{1}{1000}+ \frac{1}{10000} +...)](https://tex.z-dn.net/?f=0%2C15%3D0%2C14999....%3D0%2C14%2B9%28+%5Cfrac%7B1%7D%7B1000%7D%2B+%5Cfrac%7B1%7D%7B10000%7D++%2B...%29)
Сумму в скобках уже подсчитали выше. Итого:
![0,14=0+ \frac{14}{100} =>0,14+ 9\frac{1}{900} = \frac{14}{100} + \frac{1}{100} = \frac{15}{100}](https://tex.z-dn.net/?f=0%2C14%3D0%2B+%5Cfrac%7B14%7D%7B100%7D+%3D%3E0%2C14%2B+9%5Cfrac%7B1%7D%7B900%7D+%3D+%5Cfrac%7B14%7D%7B100%7D+%2B+%5Cfrac%7B1%7D%7B100%7D+%3D+%5Cfrac%7B15%7D%7B100%7D+)
Вычисляем <span>0,2(3)-0,(15):
![\frac{23}{100} - \frac{15}{100} = \frac{8}{100} = \frac{2}{25}](https://tex.z-dn.net/?f=+%5Cfrac%7B23%7D%7B100%7D+-+%5Cfrac%7B15%7D%7B100%7D+%3D+%5Cfrac%7B8%7D%7B100%7D+%3D+%5Cfrac%7B2%7D%7B25%7D)
</span>