х---наименьшее расстояние отношение: 90/300=270/х. х=900см. ответ:900см
.................................
Всё по формулам суммы разности синусов и косинусов
1) 2sin2a*cosa
2) 2cos5a/2*cos(-a/2)=<span>2cos5a/2*cos(a/2)</span>
3) -2sin(-a/2)*sin(2a)=<span>2sin(a/2)*sin(2a)
4) 2sin(-2a)*sin(3a)=-</span>2sin(2a)*sin(3a)
![\lim\limits_{x\to 1}} \dfrac{x^3+x^2-5x+3}{x^3-x^2-x+1} =\dfrac{1^3+1^2-5\cdot1+3}{1^3-1^2-1+1} =\left[\dfrac{0}{0} \right]](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%5Cto+1%7D%7D+%5Cdfrac%7Bx%5E3%2Bx%5E2-5x%2B3%7D%7Bx%5E3-x%5E2-x%2B1%7D+%3D%5Cdfrac%7B1%5E3%2B1%5E2-5%5Ccdot1%2B3%7D%7B1%5E3-1%5E2-1%2B1%7D+%3D%5Cleft%5B%5Cdfrac%7B0%7D%7B0%7D+%5Cright%5D)
Для раскрытия неопределенности разложим числитель и знаменатель на множители:
![x^3+x^2-5x+3=x^3-x^2+2x^2-2x-3x+3=\\=x^2(x-1)+2x(x-1)-3(x-1)=(x-1)(x^2+2x-3)=\\=(x-1)(x^2-x+3x-3)=(x-1)(x(x-1)+3(x-1))=\\=(x-1)(x-1)(x+3)=(x-1)^2(x+3)](https://tex.z-dn.net/?f=x%5E3%2Bx%5E2-5x%2B3%3Dx%5E3-x%5E2%2B2x%5E2-2x-3x%2B3%3D%5C%5C%3Dx%5E2%28x-1%29%2B2x%28x-1%29-3%28x-1%29%3D%28x-1%29%28x%5E2%2B2x-3%29%3D%5C%5C%3D%28x-1%29%28x%5E2-x%2B3x-3%29%3D%28x-1%29%28x%28x-1%29%2B3%28x-1%29%29%3D%5C%5C%3D%28x-1%29%28x-1%29%28x%2B3%29%3D%28x-1%29%5E2%28x%2B3%29)
![x^3-x^2-x+1=x^2(x-1)-(x-1)=(x-1)(x^2-1)=\\=(x-1)(x-1)(x+1)=(x-1)^2(x+1)](https://tex.z-dn.net/?f=x%5E3-x%5E2-x%2B1%3Dx%5E2%28x-1%29-%28x-1%29%3D%28x-1%29%28x%5E2-1%29%3D%5C%5C%3D%28x-1%29%28x-1%29%28x%2B1%29%3D%28x-1%29%5E2%28x%2B1%29)
![\lim\limits_{x\to 1}} \dfrac{x^3+x^2-5x+3}{x^3-x^2-x+1} =\lim\limits_{x\to 1}} \dfrac{(x-1)^2(x+3)}{(x-1)^2(x+1)} =\lim\limits_{x\to 1}} \dfrac{x+3}{x+1}=\dfrac{1+3}{1+1} =\dfrac{4}{2} =2](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%5Cto+1%7D%7D+%5Cdfrac%7Bx%5E3%2Bx%5E2-5x%2B3%7D%7Bx%5E3-x%5E2-x%2B1%7D+%3D%5Clim%5Climits_%7Bx%5Cto+1%7D%7D+%5Cdfrac%7B%28x-1%29%5E2%28x%2B3%29%7D%7B%28x-1%29%5E2%28x%2B1%29%7D+%3D%5Clim%5Climits_%7Bx%5Cto+1%7D%7D+%5Cdfrac%7Bx%2B3%7D%7Bx%2B1%7D%3D%5Cdfrac%7B1%2B3%7D%7B1%2B1%7D+%3D%5Cdfrac%7B4%7D%7B2%7D+%3D2)