1)
![y=sinx](https://tex.z-dn.net/?f=y%3Dsinx)
; [
![\frac{ \pi }{6} ; \frac{7 \pi }{6}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%3B+%5Cfrac%7B7+%5Cpi+%7D%7B6%7D+)
]
![y'=(sinx)'=cosx](https://tex.z-dn.net/?f=y%27%3D%28sinx%29%27%3Dcosx)
Найдем критические точки:
![cosx=0](https://tex.z-dn.net/?f=cosx%3D0)
![x= \frac{ \pi }{2} + \pi n](https://tex.z-dn.net/?f=x%3D+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B+%5Cpi+n)
, n<span>∈ <span>Z
</span></span>
![\frac{ \pi }{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+)
входит в отрезок, поэтому найдем значение функции этой точке:
![y(x)=sin \frac{ \pi }{2} =](https://tex.z-dn.net/?f=y%28x%29%3Dsin+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%3D)
1
<span>Вычислим значения функции на концах отрезка:
</span>
![y( \frac{ \pi }{6} )=sin \frac{ \pi }{6} =](https://tex.z-dn.net/?f=y%28+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%29%3Dsin+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%3D)
<span>0.5
</span>
![y( \frac{7 \pi }{6} )=sin \frac{7 \pi }{6} =](https://tex.z-dn.net/?f=y%28+%5Cfrac%7B7+%5Cpi+%7D%7B6%7D+%29%3Dsin+%5Cfrac%7B7+%5Cpi+%7D%7B6%7D+%3D)
<span>-0.5
</span>Ответ:
![max_{[ \frac{ \pi }{6}; \frac{7 \pi }{6} ]} =1](https://tex.z-dn.net/?f=++max_%7B%5B+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%3B+%5Cfrac%7B7+%5Cpi+%7D%7B6%7D++%5D%7D+%3D1)
;
![min_{[ \frac{ \pi }{6}; \frac{7 \pi }{6} ]} =-0.5](https://tex.z-dn.net/?f=+min_%7B%5B+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%3B+%5Cfrac%7B7+%5Cpi+%7D%7B6%7D++%5D%7D+%3D-0.5)
2)
![y=sinx](https://tex.z-dn.net/?f=y%3Dsinx)
,
![[- \frac{2 \pi }{3}; \frac{ \pi }{2} ]](https://tex.z-dn.net/?f=%5B-+%5Cfrac%7B2+%5Cpi+%7D%7B3%7D%3B+%5Cfrac%7B+%5Cpi+%7D%7B2%7D++%5D)
![y'=(sinx)'=cosx](https://tex.z-dn.net/?f=y%27%3D%28sinx%29%27%3Dcosx)
Найдем критические точки:
![cosx=0](https://tex.z-dn.net/?f=cosx%3D0)
![x= \frac{ \pi }{2} + \pi n](https://tex.z-dn.net/?f=x%3D+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B+%5Cpi+n)
, n∈<span>Z
</span>
![\frac{ \pi }{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+)
входит в отрезок, поэтому найдем значение функции в этой точке:
![y(x)=sin \frac{ \pi }{2} =](https://tex.z-dn.net/?f=y%28x%29%3Dsin+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%3D)
<span>1
</span>Вычислим значения функции на концах отрезка:
![y(- \frac{2 \pi }{3} )=sin(- \frac{2 \pi }{3} )= \frac{- \sqrt{3} }{2}](https://tex.z-dn.net/?f=y%28-+%5Cfrac%7B2+%5Cpi+%7D%7B3%7D+%29%3Dsin%28-+%5Cfrac%7B2+%5Cpi+%7D%7B3%7D+%29%3D+%5Cfrac%7B-+%5Csqrt%7B3%7D+%7D%7B2%7D+)
≈
-0.9
1
Ответ:
![max_{[- \frac{2 \pi }{3}; \frac{ \pi }{2} ]} =1](https://tex.z-dn.net/?f=+max_%7B%5B-+%5Cfrac%7B2+%5Cpi+%7D%7B3%7D%3B+%5Cfrac%7B+%5Cpi+%7D%7B2%7D++%5D%7D+%3D1)
![min_{[- \frac{2 \pi }{3}; \frac{ \pi }{2} ]}= \frac{- \sqrt{3} }{2}](https://tex.z-dn.net/?f=+min_%7B%5B-+%5Cfrac%7B2+%5Cpi+%7D%7B3%7D%3B+%5Cfrac%7B+%5Cpi+%7D%7B2%7D++%5D%7D%3D+%5Cfrac%7B-+%5Csqrt%7B3%7D+%7D%7B2%7D++)
≈
-0.9
100% все поле
100-40=60
20% от 60 это
60:100=0.6 1%
0.6*20=12 20%
60-12=48 невспаханная часть
ответ 48
<span>1/17^x-1=1/17^-x
</span>x-1=-x
2x=1
x=1/2