Comments by "Fhf Fhf" (@fhffhff) on "Подкаст Глеба Соломина" channel.

  1. cossinx*sincosx=-sinsinx*cosx*sincosx-cossinx*coscosx*sinx -cossinxsincosx+si nsinx*sinxsincosx+(2sinsinxsinx-cossimx)coscosxcosx
    1
  2. (1-c)²-3ab=1+c ab=-c+c²/3 {b=1-c-a,a(1- c-a)=-c+c²/3; -a²+a(1-c)+c-c²/3=0 a=(1-c ±√(1+2c-c²/3))/2 b=(1-c-+√(1+2c-c²/3))/2 (c-3-√12)(c-3+√12)≤0 c[3-√12;3+√12]
    1
  3. c=3c1 4=3(c1-1)²+n² c1-1[-1;1] c1=0;1;2 n=1;2;1 c=0;3;6 a=1;0 a=0;-2 a=-2;-3 b=0;1 b=-2;0 b=-3;-2 {(0;1)(1;0)(0;-2)(-2;-3)(-3;-2)}
    1
  4. a=-b±√(4b²+37) 37=(n-2b)(n+2b) [{n=19,b=9;{n=19,b=-9;{n=-19,b=9;{n=-19, b=-9; a=-9±19=10;-28 a=9±19=28;-10
    1
  5. y^(1/(y+2))=x^(1/x²) e^(lny/(y+2))(1/y/(y+ 2)-lny(y+2)-²)=0 1+2/y-lny=0 y=4,3+*->y max=4,3^(1/6,3) e^(lnx/x²)(1-2lnx)x-³=0 x=e^0,5(•->x max=e^(0,5/e) 4,3^(1/6,3) >e^(0,5/e) y=1,x=1; y=2,x=2;(-2;-2){(1;1)(2;2)(&2;-2)}
    1
  6. z=(√2±√2i)/2 z⁷=cos(45°•7/±isin(45°•7)= √2/2-+i√2/2 z⁷+1/z⁷=√2/2
    1
  7. $√2/2(-cos(π/4-x)+1,5/cos(π/4-x))/cos³x dx=-0,5tgx-3$1/(cos2x+1)/cos2xdx+1,5 ln|u-√0,5|+1,5ln|u+√0,5|-3ln|u|+0,75u-²+u ²/2=-0,5tgx-3ctg(x-π/4)/2/cos2x-3/8sin ²(x-π/4)+3/4ln|cos(x-π/4)|-3/4ln|sin(x-π/4)|+1,5ln|cosx-√0,5|+1,5ln|cosx+√0,5|-3ln|cosx|+1,25/cos²x+c cosx=u x=±arccosu dx=-+1/√(1-u²)du 0,75=A(u⁴+√0,5u³)+B(u⁴-√0,5u³)+C(u⁴-0,5 u²)+D(u³-0,5u)+E(u²-0,5){B=1,5,A=1,5, C=- 3,D=0,E=-1,5;
    1
  8. {-1/3x'(t)+2/3x=y,x''(t)-2x'(t)-3x=-3e^t. k2-2k-3=0 k=1_2=3;-1 x0=c1e^3t+c2e^-t x(t)=ce^t ce^t-2ce^t-3ce^t=-3e^t c=3/4 x(t)=c1e^3t+c2e^-t+3/4e^t y(t)=-1/3c1e^3t+c2e^-t+1/4e^t
    1