Comments by "Fhf Fhf" (@fhffhff) on "БОРИС БОЯРШИНОВ СО ДНА НАУКИ" channel.

  1. 484/49=9,88>9,81
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  2. A²(((a²-ab+2b²)√(-a²b²+144a²+144b²)+2a³ b-144a²-5ab³+3b⁴-144b²)²+(a⁴+2a³b-144a² -2ab³+b⁴-144b²)²b²=64(2a⁴+4a³b-288a²-4 ab³+2b⁴-288b²)² -112a⁸+4a⁸b²+8a⁷b³-2176a⁷b+328*288a⁶-21a⁶b⁴-448a⁶b²+12a⁵b⁵+160a⁵b³+255*576a⁵b-6a⁴b⁶+1680a⁴b⁴+184*288a⁴b²-246*144²a⁴-26a³b⁷+21a³b⁶-272a³b⁵+256*112a³b³+13a²b⁸-1580a²b⁶-511*144²a²b²+400*288a²b⁴+576ab⁷-256*576ab⁵+b¹⁰-544b⁸+328*288b⁶-256*144²b⁴=(288a⁴+288a²b²-6a²b⁴ -4ba⁵+10a³b³)(144a²+144b²-a²b²)⁰,⁵(a²+2 b²-ab)
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  3. log2¹/¹²(3/2)=7 log2¹/¹²(√5/2)=1 83/92~ 2 log2¹/¹²(5¹/⁴)=6 175/184~7
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  4. V=1/3π(b²+ba+a²)h-2/3πr³ H=bh/(b-a)
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  5. M1M2(8;0;7)M1M3(7;-5;1)M1M4(9;2;1) |8 0 7|=-40+0+98-(-35*9)-0-16=357 |7 -5 1| |9 2 1| V=1/6*357=59,5
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  6. $r²dm=4πp$r⁴dr=4πpr⁵/5(0;R)=3mR²/5 1/3pπh/(b-a)$(a;b)3r⁴dr=πph(b⁴+b³a +..+a⁴)/5=3m/5(b²+(a³b+a⁴)/(a²+ab+b²)) I=1/5πp(h(b⁵+b3a+b²a²+a³b+a⁴)-4R⁵) 1/3π(a²+ab+b²)h
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  7. √х^log(2)√x≥2,√x>0,x>0.x^(0,25log(2)x)≥2,[{xє(0;1),0,25log(2)x≤log(x)2;(1){x>1,0,25log(2)≥log(x)2;(1):0,25log(2)x-1/log(2)x≤0,(log²(2)x-4)/log(2)x≤0,(log(2)x 2)(log(2)x+2)/log(2)x≤0*-2+ 0°-*+2>log (2)x log(2)xє(-∞;-2]U(0;2],хє(0;1/4]U(1;4][xє(0;1/4],{x>1,хє[1/4;1)U[4;+∞);[xє(0;1/4],хє[4;+∞);xє(0;1/4]U[4;+∞)
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  8. X²+8x+7,5=±8,5[x²+8x-1=0,x²+8x+16=0;[x=-4±√17,x=-4.
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  9. z'(x)=1/(1+(xy²)²)y²=1/5 z'(y)=1/(1+(xy²)²)*2xy=4/5 gradz(A)=1/5i+4/5j (1/(1+(xy²)²)y²dx+1/(1+(xy²)²)*2xydy)/d(3i+ 4j)=1/√17+4/√17=5/√17
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  10. y=√(-x²+ax) y=√(-x2+2ax) [a=0,x=0; 2$(0;a)dx$(√(-x²+ax);√(-x²+2ax))(x²+y²)dy =2$(0;r)(r'cosф-rsinф)dф$(√(-r²cosф²+ar cosф);√(-r²cos²ф+2arcosф))r²(r'sinф+rcosф)dф=2$(0;a)((2x²/3+2ax/3)(-(x-a)²+a²) ⁰,⁵-(2/3x²+ax/3)√(-(x-a/2)²+a²/4))dx=-1/4 a⁴arcsin(-(x/a-1)²+1)⁰,⁵+1/3a²(-(x-a)²+a²) ⁰,⁵(x-a)-1/6(-(x-a)²+a²)⁰,⁵(x-a)³+a(-(x-a)²+ a²)¹,⁵/3-1/3a⁴arcsin((x-a)/a)-(x-a)a²(-(x-a) ²+a²)⁰,⁵/3-1/6√(-(x-0,5a)²+a²/4)(x-a/2)(2a- ¹(x-a/2)²-a/4)+3/32a³arcsin√(-(2x/a-1)²+ 1)-1/3a√(-(x-a/2)²+a²/4)(x-a/2)+1/96√(- (x-a/2)²+a²/4)³)|(0;a)*2=-1/6a⁴*π*2=-π/3a⁴ x=rcosф,у=rsinф r=аcosф r=2acosф (-(x/a-1)²+1)⁰,⁵=sinu x/a=1±cosu d(x/a)=-+sin udu √(-(2x/a-1)²+1)=sinu x=a/2(1±cosu) dx=-+a/2sinudu
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  11. y=±√(1-x2) √(x²-x⁴)≤1/2,≥-1/2
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  12. {(±11;±10)(±5;±2)}
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  13. e^(-lnx*e^(xlnx))(-e^(xlnx))(x-¹+lnx (lnx+1))=0->x x=2^-2(2^(1/2)=2^0,5)
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  14. x*4x²(1+27x³)+x²(1+8x³)*3x+(1+x³) *2x*9x²-(1+x³)*4x²*3x-x²*2x(1+27x³)-x(1+8x³)*9x²=x³*2+12x⁶=10 (x³+1)(6x³-5)=0 x=-1;(5/6)¹/³
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  15. log(2-x)(a^(x+2)+2a^(1-x)+x-1)+log(2+x)(a^(-x+2)+2a^(1+x)-x-1)=2{2-x>0,2-x≠1,2+x>0,2+x≠1;{x<2,x≠1,x>-2,x≠-1;хє(-2;-1)U (-1;1)U(1;2)(a^2xa²+2a)/a^x≥2a√(2a) (a² +2a*a^2x)/a^x≥2a√(2a) {2a√(2a)-3>0;2a √(2a)-3>0;(2a)¹,⁵>3,2a>3^(2/3),a>0,5*3^ (2/3) ає[0,5;1]U[e;+∞)
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  16. x³/3lna+x3/3lnx-x³/9+c
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  17. $x²e^(ax)dx=e^(ax)(a0x²+a1x+a2)+c=e^ (ax)(1/ax²-2/a²x+2/a³)+c e^(ax)(aa0x²+(aa1+2a0)x+aa2+a1)=x²e^ (ax){a0=1/a,a1=-2/a²,a2=2/a³;
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  18. |i j k| |3 7 -2|=33i-17j-10k |1 -1 5| l=√(33²+17²+10²)=√1478 S=0,5√1478
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  19. ln²y/2=-ln|tg(π/4-x/2)|+c y=e^±√(-2ln|tg (π/4-x/2)|+2c)
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  20. $(0;≠)(12,5lnt-1,25ln(t¹⁰+1))dt=12,5(t lnt-t)-1,25En=1;∞(-1)^(n-1)/n*t^(10n +1)/(10n+1)(0;=)~0, по-любому сходится
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  21. a+c+d-e-h a,b,c,d e,a-d+e+f-g h,f,g,a+b+c+d-f-g-h b+c+d-e-f a+c-g=h a+b+c+d=22 4 1,2,7,12 e=11 11,5 f=8 5,8,3,6 g=3 2 Можно, только не получилось.
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  22. limx->0(1+x+x²)/(3-x²)=1/3 limx->02(0,5x)²/x²=0,5 limx->0 2sin²(0,5x)/x²=0,5
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  23. limx->0(sin1,5x/sin(0,5x))=3 limx->3(1/(x²-5x+7)*(2x-5))=1
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  24. limn->∞1/(1-1/3)/(1/(1-1/4))=1,5/(4/3)=1,125 limn->∞(1+n)/2*n/((1+2n-1)/2*n)=1/2
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  25. $(-R;R)dx$(-√(R²-x²);√(R²-x²))2√(R²-x²)dy= 4(R²x-x³/3)(-R;R)=4(R³-R3/3)-4(-R³+R³/3)= 16/3R³ V=(2π+16/3)R³
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  26. a²+(x-2021)²=|x-a-2021|-|x+a-2021|,[{x≥a+ 2021,a²+(x-2021)²=-2a;{хє[-а+2021;а+2021);a²+(x-2021)²=-2x+ 4042;{х<-а+2021,a²+(x-2021)²=2a;[{x≥a+ 2021,x=2021±√(-а(а+2))+*-2-*+0>а;{хє[-а+2021;а+2021);x²-4040х+2021²-4042+а²=0;{х<-а+2021,x=2021±√(-а²+2a);[а=0,х=2021,{хє[-а+2021;а+2021), х=2020±√(1-а²);{х<-а+2021,ає(0;1), a(a-1)<0 +0°-°1+>a;[a=0,x=2021,aє[0;1],х= 2020±√(1-а²);ає(0;1),х=2021-√(-а(а-2));
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  27. log²(2)(x+1)/(2x-1)-log(2)(x+1)/(2x-1)≤0 y=log(2)(x+1)/(2x-1) y(y-1)≤0+*0-*1+>y ує(-∞;0]U[1;+∞) [{(x+1)/(2x-1)>0,(x+1)/(2x-1)≤1,(x+1)/(2x-1)≥2;[{(x+1)/(x-1/2)>0, +°-1-°+0,5>x (x-2)/(x-1/2)≥0+°0,5-*+2>x;(x-1)/(x-1/2)≤0+°0,5-*1+>x;[{хє(-∞;-1)U(0,5;+∞),хє(-∞;0,5)U[2;+∞); хє(0,5;1];[хє(-∞;-1)U[2;+∞),хє(0,5;1];хє(- ∞;-1)U(0,5;1]U[2;+∞)
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  28. (x+1)(x²-x+1)(x²+x+1)=(√2+2)(3+ √2)(5+3√2)=65+39√2
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  29. А когда такое было,что в гостях у него были шизофреники.
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  30. (x-1/3)³-1/3(x-1/3)-47/64/27=0 x-1/3=(47/2+√(47²-128²)/2)¹/³/12+(..-..)..=2/3cos(1/3arccos(47/128)+2/3πn) x=1/3+2/3cos(1/3arccos(47/128)+2/3πn)
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  31. {5|x|+12|y-2|=60,y²-a²=4(y-1)-x²;[{y=7-5/12x,x≥0,y≥2;{y=-3+5/12x,x≥0,y≤2;{y=7+5/12x,x≤0,y≥2;{y=-3-5/12x,x≤0,y≤2;y ²-4y-a²+4+x²=0;y=2±√(a²-x²);ує[-3;7] √(а²- х²)≤5,а²≤25+х²,≥х² а²≥0,≤169,ає[-13;13] 2-√(а²-х²)≥-3,√(а²-х²)≤5 ає[-13;13]
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  32. lgx=y,(z-1)(z²+z+4)=0 z=1;-1/2±√3,75i y=1±√3 x=10^(1±√3)
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  33. x≠2;3;-4;-5 x²+7x+11=±(x²-7x+11)[x=0,2x²+22=0;{0}
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  34. v(x)(u(x)-1)=∞•0=v(x)lnu(x)=-∞ e^-∞=0 v'(x)=-v(x)/u(x)*u'(x)/lnu(x)
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  35. limx->π/2(sin(π/2-x)/2/(π/2-x))=1/2
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  36. limx->0(-1,5/(x-1/2)²)=-6
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  37. limx->0(1,5x*(-0,5x))/(3x*(-2x))=0,125
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  38. x(√(x²-1)-x)=x(-0,5x-¹+..)=-0,5;x->-∞=∞-
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  39. ln->∞(4^n*√π(1/4)^n)=√π
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  40. /_2=arctg(a/b/3) /_1=arctg(1/3a/b) /_2=/_1✓
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  41. [10²⁰'⁰⁰⁰/(10¹⁰⁰+3)]=10¹⁹'⁹⁰⁰-3*10¹⁹'⁸ ⁰⁰+..-3¹⁹⁹+[9¹⁰⁰/(10¹⁰⁰+3)] -3¹⁹⁹=-3³=1mod10✓ 10(1-1/2)(1-1/5)=4
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  42. {0,5log|x|2>1,x²>0,x²≠1;{(0,5-log(2)|x|)/log(2)|x|>0,x≠0,x≠±1;{(log(2)|x|-0,5)/log(2)|x|<0,+1°2⁰,⁵-°+>|x| |x|є(-∞;1)U(2⁰,⁵;+∞) хє(-∞;-2⁰,⁵)U(-1;1)U(2⁰,⁵;+∞) хє(-∞;- 2⁰,⁵)U(-1;0)U(0;1)U(2⁰,⁵;+∞)
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  43. 5^(√x/2)-5^(√y/2)=625-25{√x/2=4, √y/2=2;{x=64,y=4.(64;4)
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  44. f=333/2/3,14√(π•0,015²/0,25/(π•0, 05²*0,2+π*0,015²*0,05))=1,95Гц
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  45. (2+√2)⁹=901*2⁵+1393*16*√2
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  46. a≥b y=b√(1-X²/A²) x=±ab/√(a²+b²) $(-ab/√(a²+b²);ab/√(a²+b²))b√(1-x²/a²)dx=b/a (0,5a²arcsin(x/a)+x√(a²-x²)/2)|(-ab/√(a²+ b²);ab/√(a²+b²))=baarcsin(b/√(a²+b²))+a²b²/(a²+b²) S∆=0,5(ab/√(a²+b²))²=0,5a ²b²/(a²+b²) S=baarcsin(b/√(a²+b²)) $..=4 abarcsin(b/√(a²+b²))
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  47. x=(x-0,5)(cos(2πn/2001)+isin(2πn/2001)),n=1..2000 x=-0,25/sin(πn/2 001)(-sin(πn/2001)+icos(πn/2001)) Ei=1;2001xi=500,25
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  48. 1402,701,700,350,175',174,87,86,43,42',21,20,10,5,4' 21+20(1/2^4-1)/(1/2-1)=60
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