Решение:
1) f'(x)=-1/(1-x)=1/(x-1)
k=-1 1/(x-1)=-1 x-1=-1 x=0
f(0)=ln1=0
y=-x
2) k=3
3/(3x-2)=3 3=9x-6 9=9x x=1
f(1)=ln1=0
y=3x+c 0=3*1+c c=-3
y=3x-3
3) f'=(2x-2)/(x^2-2x-3)
3y=1-2x y=-2/3x+1/3
(x-1)/(x^2-2x-3)=-1/3
3x-3=-x^2+2x+3
x^2+x-6=0
x=-3 x=2
y(2)=ln(-3) не существует
y(-3)=ln(9-3+6)=ln12
ln12=-2/3(-3)+c
ln12=2+c x=ln12-2
y=-2/3x+ln12-2
4) (-2x-2)/(3-2x-x^2)
2/3x-1/3=y
(x+1)/(x^2+2x-3)=1/3
3x+3=x^2+2x+3
x^2-x=0
x=1 x=0
f(0)=ln3
y=2/3x+c
y=2/3x+ln3.
<span>3cos^2a-8/5 если sin^2 a=1/5
</span>3(1-sin^2 a)-8/5 если sin^2 a=1/5
12/5-8/5=4/5
Отв: 4/5
Sin(2arccos1/4)=2sin(arccos1/4)cos(arccos1/4)=2sqrt(1-1/16)*1/4=2sqrt(15)/16*1/4=sqrt(15)32
А) (2х-3у)(2х+3у) = ![4x^2+6xy-6xy-9y^2=4x^2-9y^2](https://tex.z-dn.net/?f=4x%5E2%2B6xy-6xy-9y%5E2%3D4x%5E2-9y%5E2)
Б) ![(a-5)^2-2a(a-3)=a^2-10a+25-2a^2+6a=-a^2-4a+25](https://tex.z-dn.net/?f=%28a-5%29%5E2-2a%28a-3%29%3Da%5E2-10a%2B25-2a%5E2%2B6a%3D-a%5E2-4a%2B25)
<span>3а+3в+с*(а+в)=3а+4в+са+св=3*(а+в)+с*(а+в)=(а+в)*(3+с)</span>
Это арифметический прогрессия
![a_{17} = \frac{ a_{15} + a_{19} }{2} = \frac{12}{2} =6](https://tex.z-dn.net/?f=+a_%7B17%7D+%3D+%5Cfrac%7B+a_%7B15%7D+%2B+a_%7B19%7D+%7D%7B2%7D+%3D+%5Cfrac%7B12%7D%7B2%7D+%3D6)