У=3+х
у=-2х
3+х=-2х
-3х=3
х=-1
у=3+(-1)=2
<em>(-1;2)</em>
Ответ 0.2 т.к. (3×0+2)/10=0+2/10=0.2
Y`=2x/π+2cos2x+1/2cosx-1/2sinx
y`(π/2)=1+2*(-1)+1/2*0-1/2*1=1-2+0-0,5=-1,5
Раскрываем модуль:
1) x^2-6x+1=2x-6, где x-3>=0; x>=3
x^2-8x+7=0
D=64-28=36=6^2
x1=(8+6)/2=7>3 - верно
x2=2/2=1<3 - неверно
2) x^2-6x+1=-2x+6, где x<=3
x^2-4x-5=0
D=16+20=36=6^2
x1=(4+6)/2=5>3 - неверно
x2=(4-6)/2=-1<3 - верно
Ответ: x1=7; x2=-1
<span>12cos<span>²</span> (2-3x) + 4 sin (2-3x) -11 = 0</span>
<span>12(1-sin<span>²(2-3x))+4sin(2-3x) -11=0</span></span>
<span><span>12-12sin<span>²(2-3x)+4sin(2-3x)-11=0</span></span></span>
<span><span><span>-12sin<span>²(2-3x)+4sin(2-3x)-11+12=0</span></span></span></span>
<span><span><span><span>12sin<span>²(2-3x)-4sin(2-3x)-1=0</span></span></span></span></span>
<span><span><span><span><span>Пусть sin(2-3x)=t, -1<t<1</span></span></span></span></span>
<span><span><span><span><span>12t<span>²-4t-1=0</span></span></span></span></span></span>
<span><span><span><span><span><span>D=16+4*12=64</span></span></span></span></span></span>
<span><span><span><span><span><span>t=4+8/24=1/2</span></span></span></span></span></span>
<span><span><span><span><span><span>t=4-8/24=-1/6</span></span></span></span></span></span>
<span><span><span><span><span><span>И делаем обратную замену</span></span></span></span></span></span>
<span><span><span><span><span><span>sin(2-3x)=1/2 sin(2-3x)=-1/6</span></span></span></span></span></span>
<span><span><span><span><span><span>Далее получаем корни..</span></span></span></span></span></span>