Составляем уравнение:
(3х-4)-(7х+6)=0
х= -2,5
1) Наверное (375/1029)^13=(125/343)^13
2) (2025/(3*3*5))^11=45^11
Определение производной:
![\displaystyle \lim_{зx \to0} \frac{f(x_0+зx)-f(x_0)}{зx}](https://tex.z-dn.net/?f=%5Cdisplaystyle++%5Clim_%7B%D0%B7x++%5Cto0%7D++%5Cfrac%7Bf%28x_0%2B%D0%B7x%29-f%28x_0%29%7D%7B%D0%B7x%7D)
![\displaystyle \lim_{зx\to0} \frac{(x_0+зx)^3-x_0^3}{зx} =\lim_{зx\to0} \frac{(x_0^3+3x_0^2зx+3x_0зx^2+зx^3)-x_0^3}{зx}=](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Clim_%7B%D0%B7x%5Cto0%7D+%5Cfrac%7B%28x_0%2B%D0%B7x%29%5E3-x_0%5E3%7D%7B%D0%B7x%7D+%3D%5Clim_%7B%D0%B7x%5Cto0%7D+%5Cfrac%7B%28x_0%5E3%2B3x_0%5E2%D0%B7x%2B3x_0%D0%B7x%5E2%2B%D0%B7x%5E3%29-x_0%5E3%7D%7B%D0%B7x%7D%3D)
![\displaystyle=\lim_{зx\to0} \frac{x_0^3+3x_0^2зx+3x_0зx^2+зx^3-x_0^3}{зx}=\lim_{зx\to0} \frac{3x_0^2зx+3x_0зx^2+зx^3}{зx}=](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D%5Clim_%7B%D0%B7x%5Cto0%7D+%5Cfrac%7Bx_0%5E3%2B3x_0%5E2%D0%B7x%2B3x_0%D0%B7x%5E2%2B%D0%B7x%5E3-x_0%5E3%7D%7B%D0%B7x%7D%3D%5Clim_%7B%D0%B7x%5Cto0%7D++%5Cfrac%7B3x_0%5E2%D0%B7x%2B3x_0%D0%B7x%5E2%2B%D0%B7x%5E3%7D%7B%D0%B7x%7D%3D)
![\displaystyle=\lim_{зx\to0}(3x_0^2+3x_0зx+зx^2)=3x_0^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D%5Clim_%7B%D0%B7x%5Cto0%7D%283x_0%5E2%2B3x_0%D0%B7x%2B%D0%B7x%5E2%29%3D3x_0%5E2)
В качестве
![x_0](https://tex.z-dn.net/?f=x_0)
примем х, т.е. осуществив замену
![x_0=x](https://tex.z-dn.net/?f=x_0%3Dx)
получим нужное.
f(x)=3sinx+2cos x
f(x)=(3sinx+2cosx)=3cosx-2sinx
первую производную = к нулю
f(x)=0
3cosx-2sinx=0 / :cosx≠0
-2tgx=-3
2tgx=3
tgx=3/2