√6*cos(π-π/4)*sin(π+π/3)=√6*(-cosπ/4)*(-sinπ/3)=√6*√2/2*√3/2=1,5
6tg(180+45)*(-sin30)=-6*tg45*1/2=-3*1=-3
4tg(3π+π/3)*tg(3π-π/6)=4*tgπ/3*(-tgπ/6)=-4*√3*1/√3=-4
Здесь будут использоваться замечательные пределы
![\displaystyle \lim_{x \to 0}\dfrac{a^x-1}{x}=\ln a;~~\lim_{x \to 0}\frac{{\rm tg}\, x}{x}=\lim_{x \to 0}\frac{{\rm arctg}\, x}{x}=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%5Cdfrac%7Ba%5Ex-1%7D%7Bx%7D%3D%5Cln%20a%3B~~%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B%7B%5Crm%20tg%7D%5C%2C%20x%7D%7Bx%7D%3D%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B%7B%5Crm%20arctg%7D%5C%2C%20x%7D%7Bx%7D%3D1)
![\displaystyle \lim_{x \to 0}\frac{10^{2x}-7^{-x}}{2{\rm tg}\, x-{\rm arctg}\, x}=\lim_{x \to 0}\frac{100^x-\dfrac{1}{7^x}}{2{\rm tg}\, x-{\rm arctg}\, x}=\lim_{x \to 0}\frac{\dfrac{1}{7^x}\left(700^x-1\right)}{2{\rm tg}\, x-{\rm arctg}\, x}=\\ \\ \\ =\lim_{x \to 0}\frac{1\cdot x \cdot (700^x-1)}{x\left(2{\rm tg}\, x-{\rm arctg}\, x\right)}=\lim_{x \to 0}\frac{x\ln700}{2{\rm tg}\, x-{\rm arctg}\, x}=\\ \\ \\ =\ln 700\lim_{x \to 0}\frac{1}{\dfrac{2{\rm tg}\, x}{x}-\dfrac{{\rm arctg}\, x}{x}}=\ln 700\cdot\frac{1}{2\cdot 1-1}=\ln700](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B10%5E%7B2x%7D-7%5E%7B-x%7D%7D%7B2%7B%5Crm%20tg%7D%5C%2C%20x-%7B%5Crm%20arctg%7D%5C%2C%20x%7D%3D%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B100%5Ex-%5Cdfrac%7B1%7D%7B7%5Ex%7D%7D%7B2%7B%5Crm%20tg%7D%5C%2C%20x-%7B%5Crm%20arctg%7D%5C%2C%20x%7D%3D%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B%5Cdfrac%7B1%7D%7B7%5Ex%7D%5Cleft%28700%5Ex-1%5Cright%29%7D%7B2%7B%5Crm%20tg%7D%5C%2C%20x-%7B%5Crm%20arctg%7D%5C%2C%20x%7D%3D%5C%5C%20%5C%5C%20%5C%5C%20%3D%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B1%5Ccdot%20x%20%5Ccdot%20%28700%5Ex-1%29%7D%7Bx%5Cleft%282%7B%5Crm%20tg%7D%5C%2C%20x-%7B%5Crm%20arctg%7D%5C%2C%20x%5Cright%29%7D%3D%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7Bx%5Cln700%7D%7B2%7B%5Crm%20tg%7D%5C%2C%20x-%7B%5Crm%20arctg%7D%5C%2C%20x%7D%3D%5C%5C%20%5C%5C%20%5C%5C%20%3D%5Cln%20700%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B1%7D%7B%5Cdfrac%7B2%7B%5Crm%20tg%7D%5C%2C%20x%7D%7Bx%7D-%5Cdfrac%7B%7B%5Crm%20arctg%7D%5C%2C%20x%7D%7Bx%7D%7D%3D%5Cln%20700%5Ccdot%5Cfrac%7B1%7D%7B2%5Ccdot%201-1%7D%3D%5Cln700)
Ответ: ln700.
X = 2 : 4/7; 2 • 7/4
x = 7/2; 3 1/2
480м - 100%
х м - 45%
х=(480*45):100=216
480-216=264м робітники проложили за другу неділю
52,28 - (4,7 - 8,72) - 3,7 + ( - 6,3 + 2,25) =
= 52,28 - 4,7 + 8,72 - 3,7 - 6,3 + 2,25 =
= 47,58 + 5,02 - 4,05 =
= 52,6 - 4,05 =
= 48,55