(Последовательность)
- не монотонная, т.к. знакочередующаяся
- |xn - A| = |xn| = 1/5^n
1 / 5^n < ε
5^n > 1/ε
n > -log5(ε)
N(ε) = [-log5(ε)]
N(0.01) = 2, т.е. для всех n >= 3 верно, что |xn| < 0.01
(Пределы)
3) Если sin(m) = 0, предел равен нулю. Иначе
![\displaystyle\lim_{x\to m}\left(\frac{\sin m}{\sin x}\right)^{\frac{\cos3\pi}{x-m}}=\lim_{x\to0}\left(\frac{\sin m}{\sin(m+x)}\right)^{-1/x}=\dots\\ \frac{\sin m}{\sin(m+x)}=\frac{\sin m}{\sin m \cos x+\cos m\sin x}\approx\frac{1}{1+x\,\mathrm{ctg}\, m} \\ \dots = \lim_{x\to0}(1+x\,\mathrm{ctg}\, m)^{1/x}=e^{\,\mathrm{ctg}\, m}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%20m%7D%5Cleft%28%5Cfrac%7B%5Csin%20m%7D%7B%5Csin%20x%7D%5Cright%29%5E%7B%5Cfrac%7B%5Ccos3%5Cpi%7D%7Bx-m%7D%7D%3D%5Clim_%7Bx%5Cto0%7D%5Cleft%28%5Cfrac%7B%5Csin%20m%7D%7B%5Csin%28m%2Bx%29%7D%5Cright%29%5E%7B-1%2Fx%7D%3D%5Cdots%5C%5C%0A%5Cfrac%7B%5Csin%20m%7D%7B%5Csin%28m%2Bx%29%7D%3D%5Cfrac%7B%5Csin%20m%7D%7B%5Csin%20m%20%5Ccos%20x%2B%5Ccos%20m%5Csin%20x%7D%5Capprox%5Cfrac%7B1%7D%7B1%2Bx%5C%2C%5Cmathrm%7Bctg%7D%5C%2C%20m%7D%20%5C%5C%0A%5Cdots%20%3D%20%5Clim_%7Bx%5Cto0%7D%281%2Bx%5C%2C%5Cmathrm%7Bctg%7D%5C%2C%20m%29%5E%7B1%2Fx%7D%3De%5E%7B%5C%2C%5Cmathrm%7Bctg%7D%5C%2C%20m%7D)
4)
![\displaystyle\lim_{x\to \pi}\frac{\cos 0.5x}{e^{\sin x}-e^{\sin 4x}}=[t=\pi-x]=\lim_{t\to0}\frac{\sin 0.5t}{e^{\sin t}-e^{-\sin 4t}}=\\=\lim_{t\to0}\frac{0.5t}{(1+t)-(1-4t)}=\lim_{t\to0}\frac{0.5t}{5t}=0.1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%20%5Cpi%7D%5Cfrac%7B%5Ccos%200.5x%7D%7Be%5E%7B%5Csin%20x%7D-e%5E%7B%5Csin%204x%7D%7D%3D%5Bt%3D%5Cpi-x%5D%3D%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Csin%200.5t%7D%7Be%5E%7B%5Csin%20t%7D-e%5E%7B-%5Csin%204t%7D%7D%3D%5C%5C%3D%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B0.5t%7D%7B%281%2Bt%29-%281-4t%29%7D%3D%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B0.5t%7D%7B5t%7D%3D0.1)
<span>5,3х+0,2х=22
5,5x=22
</span>x= 22/5,5= (переносим запятую)220/55=4
x=4
х3-5х2-4х+20=0;
х3-5х2-4х= -20;
3х-10х-4х=-20;
-11х=-20;
11х=20;
х=1 дробь числитель 9 знаменатель 11
удачи))))
Всего 8кор по 3кг
Сварено 14 кг
Осталось ?
8*3=24
24-14=10кг
Х лет сыну,
х+2 - дочери,
х+29 - отцу,
х+29-3 - матери.
х+х+2+х+29+х+26=77,
4х+57=77,
4х=77-57,
5х=20,
х=20:4,
х=5;
х+2=5+2=7,
х+29=5+29=34,
34-3=31.