6x-3+15-5x=6*1,5-3+15-5*1,5=9-3+15-7,5=6+7,5=13,5
Ответ:
1) ∆ВСН, <ВНС=90°.
ВН=½ВС, поэтому <ВСН, лежащий напротив катета ВН, равен 30°
2) <С=<ВСН+<АСН=90°
<АСН=90°-<ВСН=90°-30°=60°
3) Сумма острых углов прямоугольного треугольника равна 90°
∆АСН, <АНС=90°
<А=90°-<АСН=90°-60°=30°
4) sinA=sin30°=½
Отвт: ½
Преобразуем: ![\sf \lim\limits_{n\to\infty}(\frac{n^{3}+n+1}{n^{3}+2})^{2n^{2}}=\lim\limits_{n\to\infty}((1+\frac{n-1}{n^{3}+2})^{n^{2}})^{2}](https://tex.z-dn.net/?f=%5Csf%20%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%28%5Cfrac%7Bn%5E%7B3%7D%2Bn%2B1%7D%7Bn%5E%7B3%7D%2B2%7D%29%5E%7B2n%5E%7B2%7D%7D%3D%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%28%281%2B%5Cfrac%7Bn-1%7D%7Bn%5E%7B3%7D%2B2%7D%29%5E%7Bn%5E%7B2%7D%7D%29%5E%7B2%7D)
Из второго замечательного предела следует:
;
Однако ![\lim\limits_{n\to\infty} (1+\frac{n-1}{n^{3}+2})^{\frac{n^{3}+2}{n-1}} = \lim\limits_{n\to\infty} (1+\frac{n-1}{n^{3}+2})^{n^{2}}=e\Rightarrow \lim\limits_{n\to\infty} (1+\frac{n-1}{n^{3}+2})^{2n^{2}}=e^{2}](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%20%281%2B%5Cfrac%7Bn-1%7D%7Bn%5E%7B3%7D%2B2%7D%29%5E%7B%5Cfrac%7Bn%5E%7B3%7D%2B2%7D%7Bn-1%7D%7D%20%3D%20%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%20%281%2B%5Cfrac%7Bn-1%7D%7Bn%5E%7B3%7D%2B2%7D%29%5E%7Bn%5E%7B2%7D%7D%3De%5CRightarrow%20%5Clim%5Climits_%7Bn%5Cto%5Cinfty%7D%20%281%2B%5Cfrac%7Bn-1%7D%7Bn%5E%7B3%7D%2B2%7D%29%5E%7B2n%5E%7B2%7D%7D%3De%5E%7B2%7D)
(√5-√3)/(√5+√3)=(√5-√3)(√5-√3)/(√5+√3)(√5-√3)=(5-2√15+3)/(5-3)=
=(8-2√15)/2=4-√15