0 name: Switch category to $module$/top/╨Я╨╛ ╤Г╨╝╨╛╨╗╤З╨░╨╜╨╕╤О ╨┤╨╗╤п joriy nazorat

11,7⁰    
=
117⁰
~
116⁰
~
118⁰
}

64608 name: ni ixchamlang.

::ni ixchamlang.::[html]
\\( \\frac\{tg2x \\cdot tgx \}\{tg2x-tgx\} \\) ni \nixchamlang.
{
~
tgx
~
sinx
~
cos2x
=
sin2x
}

64605 name: nuqtani hosil qilish uchun (1;0) nuqtani O nuqta atrofida necha gradusga burish kerak?

::nuqtani hosil qilish uchun (1;0) nuqtani O nuqta atrofida necha gradusga burish kerak?::[html]
 \\( ( \\frac\{ \\sqrt[]\{3\} \}\{2\}; \\frac\{1\}\{2\} ) \\) nuqtani hosil qilish uchun (1;0) nuqtani O\nnuqta atrofida necha gradusga burish kerak?
{
=
\\( \\frac\{ \\pi \}\{6\} \\)
~
-\\( \\frac\{ \\pi \}\{6\} \\)
~
\\( \\frac\{ \\pi \}\{3\} \\)
~
\\( 2 \\pi \\)
}

64607 name: Sonlarni kamayish tartibida yozing: a=cos2; b=cos2^0; c=sin2^0; d=sin2

::Sonlarni kamayish tartibida yozing\: a\=cos2; b\=cos2^0; c\=sin2^0; d\=sin2::[html]
Sonlarni kamayish tartibida yozing\: a\=cos2; b\=cos2⁰ ;  c\=sin2⁰ ; d\=sin2
{
~
a>c>d>b
~
d>c>b>a
=
b>c>d>a
~
c>d>b>a
}

64606 name: tg╬▒=тИЪ5 boтАШlsa, sin2╬▒ ni toping.

::tg╬▒\=тИЪ5 boтАШlsa, sin2╬▒ ni toping.::[html]
\\( tg \\alpha\= \\sqrt[]\{5\} \\) boтАШlsa,\\( sin2 \\alpha \\) ni toping.
{
~
\\( \\frac\{ 3\\sqrt[]\{5\} \}\{5\} \\)
~
-\\( \\frac\{ \\sqrt[]\{5\} \}\{3\} \\)
~
\\( \\sqrt[]\{5\} \\)
=
\\( \\frac\{ \\sqrt[]\{5\} \}\{3\} \\)
}

0 name: Switch category to $module$/top/╨Я╨╛ ╤Г╨╝╨╛╨╗╤З╨░╨╜╨╕╤О ╨┤╨╗╤П Joriy nazorat

$CATEGORY: $module$/top/╨Я╨╛ ╤Г╨╝╨╛╨╗╤З╨░╨╜╨╕╤О ╨┤╨╗╤П Joriy nazorat

62094 name: . a тГЧ(2;4) va b тГЧ(-6;3) vektorlarga qurilgan parallellogrammning yuzasi necha kvadrat birlikka teng?

::. a тГЧ(2;4) va b тГЧ(-6;3) vektorlarga qurilgan parallellogrammning yuzasi necha kvadrat birlikka teng?::[html]
\\( \\vec\{a\}(2;4) \\)  va \\( \\vec\{b\}(-6;3) \\) \n \n vektorlarga qurilgan parallellogrammning\nyuzasi necha kvadrat birlikka teng?
{
~
20
=
30
~
25
~
32
}

62090 name: . a тГЧ=((1;7) ) тГЧ va b тГЧ=((4;4) ) тГЧ vektorlar berilgan. x ning qanday qiymatlarida (b тГЧ+xa тГЧ ) vektor b тГЧ vektorga perpendikulyar boтАШladi?

::. a тГЧ\=((1;7) ) тГЧ va b тГЧ\=((4;4) ) тГЧ vektorlar berilgan. x ning qanday qiymatlarida (b тГЧ+xa тГЧ ) vektor b тГЧ vektorga perpendikulyar boтАШladi?::[html]
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n
\\( \\vec\{a\}\=( \\vec\{1;7\} ) \\) va \\( \\vec\{b\}\=( \\vec\{4;4\} ) \\) \n \n vektorlar berilgan. x ning qanday qiymatlarida \\( ( \\vec\{b\}+x \\vec\{a\} ) \\)\n \n vektor \\( \\vec\{b\} \\)\n \n vektorga perpendikulyar boтАШladi?
{
~
-2
~
2
=
-1
~
1
}

62088 name: . a тГЧ=((1;8) ) тГЧ va b тГЧ=((4;4) ) тГЧ boтАШlsa, |a тГЧ+b тГЧ | ifodalarning qiymatlarini toping.

::. a тГЧ\=((1;8) ) тГЧ va b тГЧ\=((4;4) ) тГЧ boтАШlsa, |a тГЧ+b тГЧ | ifodalarning qiymatlarini toping.::[html]
\\( \\vec\{a\}\=( \\vec\{1;8\} ) \\)  va \\( \\vec\{b\}\=( \\vec\{4;4\} ) \\) \n \n boтАШlsa, \\( \\left| \\begin\{matrix\} \\vec\{a\}+ \\vec\{b\} \\end\{matrix\} \\right| \\) \n \n ifodalarning qiymatlarini toping.
{
~
10
=
13
~
12
~
15
}

62093 name: a тГЧ(k+3;7) vektorning uzunligi 25 ga teng boтАШlsa, k qabul qilishi mumkin boтАШlgan qiymatlarini yigтАШindisi nechaga teng?

::a тГЧ(k+3;7) vektorning uzunligi 25 ga teng boтАШlsa, k qabul qilishi mumkin boтАШlgan qiymatlarini yigтАШindisi nechaga teng?::[html]
\\( \\vec\{a\}(k+3;7) \\)  vektorning uzunligi 25 ga teng boтАШlsa, k \n \n qabul
qilishi mumkin\nboтАШlgan qiymatlarini yigтАШindisi nechaga teng?
{
=
-6
~
3
~
21
~
15
}

62067 name: Agar a тГЧ=((k+1;-2)) тГЧ va b тГЧ=((3;k+2)) тГЧ vektorlar oтАШzaro perpendikulyar boтАШlsa, k ni toping.

::Agar a тГЧ\=((k+1;-2)) тГЧ va b тГЧ\=((3;k+2)) тГЧ vektorlar oтАШzaro perpendikulyar boтАШlsa, k ni toping.::[html]
Agar \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \\( \\vec\{a\}\= (\\vec\{k+1;-2\}) \\) va \\( \\vec\{b\}\=( \\vec\{3; k+2\} ) \\)\n \n vektorlar oтАШzaro perpendikulyar boтАШlsa, k ni toping.
{
=
1
~
2
~
-1
~
0
}

62089 name: k ning qanday qiymatlarida a тГЧ=((k+1;-2)) тГЧ va b тГЧ=((k+2; 3)) тГЧ vektorlar oтАШzaro yoтАШnalishdosh boтАШladi?

::k ning qanday qiymatlarida a тГЧ\=((k+1;-2)) тГЧ va b тГЧ\=((k+2; 3)) тГЧ vektorlar oтАШzaro yoтАШnalishdosh boтАШladi?::[html]
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \nk ning qanday qiymatlarida \n \n \\( \\vec\{a\}\=( \\vec\{k+1;-2\} ) \\) va \\( \\vec\{b\}\=( \\vec\{k+2;3\} ) \\) \n \n vektorlar oтАШzaro yoтАШnalishdosh boтАШladi?
{
=
-1,4
~
2
~
1,2
~
1,4
}

62092 name: m ning qanday qiymatida \( \vec{a}(m-1;-4) \) vektorninig uzunligi 5 dan oshmaydi?

::m ning qanday qiymatida \\( \\vec\{a\}(m-1;-4) \\) vektorninig uzunligi 5 dan oshmaydi?::[html]
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \nm ning qanday qiymatida \\( \\vec\{a\}(m-1;-4) \\) \n \n vektorninig
\n\n
 uzunligi 5 dan oshmaydi?
{
~
\\( -2< m <4 \\)
~
\\( -3 \\leq m \\leq3 \\)
~
\\( m \\leq 4 \\)
=
\\( -2 \\leq m \\leq4 \\)
}

0 name: Switch category to $module$/top/По умолчанию для Joriy nazorat

$CATEGORY: $module$/top/По умолчанию для Joriy nazorat

59550 name: f(x) funksiya x=x0 nuqtada uzluksiz deyiladi, agarda ...

::f(x) funksiya x\=x0 nuqtada uzluksiz deyiladi, agarda ...::[html]
f(x) funksiya x\=x₀  nuqtada uzluksiz deyiladi, agarda ...
{
=
\\( \\lim_\{x \\rightarrow x_\{0\}\}f(x)\=f(x_\{0\}) \\)

~
\\( \\lim_\{x \\rightarrow x_\{0\}\}f(x)\=a \\)

~
\\( \\lim_\{x \\rightarrow x_\{0\}\}f(x)\= \\infty \\)

~
Mavjud emas

}

59548 name: limitni hisoblang

::limitni hisoblang::[html]
\\( \\lim_\{x \\rightarrow 0\}\\frac\{7x\}\{sin 7x\} \\) limitni hisoblang
{
=
1

~
0

~
2/3

~
-1/3

}

59549 name: limitni hisoblang

::limitni hisoblang::[html]
   \\( \\lim_\{x \\rightarrow 0\}\\frac\{2arcsinx\}\{5x\} \\)  limitni hisoblang
{
=
2/5

~
0

~
1

~
-1/3

}

59553 name: Limitni hisoblang

::Limitni hisoblang::[html]
Limitni hisoblang  \\( \\lim_\{x \\rightarrow 1/2\}\\frac\{\{8x^3-1\}\}\{3x^2+5x+11\} \\)
{
=
0

~
3

~
-1

~
-1/3

}

59554 name: Limitni hisoblang

::Limitni hisoblang::[html]
Limitni hisoblang \\( \\lim_\{x \\rightarrow -2\}\\frac\{\{x^2-4\}\}\{x^2+3x+2\} \\)
{
=
4

~
0

~
-1

~
\\( \\infty \\)

}

59556 name: Limitni hisoblang

::Limitni hisoblang::[html] Limitni hisoblang  \\( \\lim_\{x \\rightarrow \\infty\} 2x(e^\{1/x\}-1) \\)
{
=
2

~
4

~
0

~
\\( \\infty \\)

}

59557 name: Limitni hisoblang

::Limitni hisoblang::[html]
Limitni hisoblang  \\( \\lim_\{x \\rightarrow -1\} \\frac\{3x^2+3x\}\{x^3+1\} \\)
{
=
-1

~
2

~
1

~
\\( \\infty \\)

}

59551 name: Limitni hisoblang.

::Limitni hisoblang.::[html]
Limitni hisoblang.  \\( \\lim_\{x \\rightarrow +\\infty\}\\frac\{\\sqrt\{4x^2+1\}\}\{5x-1\} \\)
{
=
2/5

~
0

~
1

~
-1/3

}

59552 name: limitni hisoblang:

::limitni hisoblang\:::[html]
Limitni hisoblang \\( \\lim_\{x \\rightarrow 1/2\}\\frac\{\{8x^3-1\}\}\{4x^2-1\} \\)  
{
~
\\( \\infty \\)

=
3/2

~
1

~
-1/3

}

59555 name: limitni hisoblang:

::limitni hisoblang\:::[html]
Limitni hisoblang\:  \\( \\lim_\{x \\rightarrow +\\infty\}(\\sqrt\{3x-7a\}-\\sqrt\{3x\}) \\)
{
=
0

~
3/x

~
\\( \\frac\{5\}\{x^2\} \\)

~
5x

}

0 name: Switch category to $module$/top/По умолчанию для Joriy nazorat

$CATEGORY: $module$/top/По умолчанию для Joriy nazorat

60044 name: Agar f(2x-1) = x3 -2x+6 bo'lsa f'(3)=?

::Agar f(2x-1) \= x3 -2x+6 bo'lsa f'(3)\=?::[html]
Agar f(2x-1) \= x³ -2x+6 bo'lsa  f'(3)\=?
{
=
5

~
6

~
1

~
0

}

60043 name: Agar f(x)=2x3 -x+1

::Agar f(x)\=2x3 -x+1::[html]
Agar f(x)\=2x³ -x+1 bo'lsa \\( f'( \\sqrt[]\{2\} )\=? \\)
{
=
11

~
10

~
4

~
0

}

60042 name: Agar f(x)=a3 bo'lsa \( f'(x)=? (a \in R ) \)

::Agar f(x)\=a3 bo'lsa \\( f'(x)\=? (a \\in R ) \\)::[html]
Agar f(x)\=a³  bo'lsa \\( f'(x)\=? (a \\in R ) \\)
{
=
0

~
3a²

~
3

~
3a

}

60046 name: Agar f(x)=ex +e2x +e3x+......+e10x bo'lsa f'(0)=?

::Agar f(x)\=ex +e2x +e3x+......+e10x bo'lsa f'(0)\=?::[html]
Agar f(x)\=e^x +e^2x +e^3x+......+e^10x        bo'lsa f'(0)\=?   
{
=
55

~
66

~
0

~
56

}

60050 name: Agar f(x)=ln(lnx) bo'lsa f'(e)=?

::Agar f(x)\=ln(lnx) bo'lsa f'(e)\=?::[html]
Agar f(x)\=ln(lnx)  bo'lsa f'(e)\=?
{
=
1/e

~
1

~
e

~
0

}

60045 name: Agar f(x)=ln(x2 -x+1) bo'lsa f'(2)=?

::Agar f(x)\=ln(x2 -x+1) bo'lsa f'(2)\=?::[html]
Agar f(x)\=ln(x² -x+1) bo'lsa f'(2)\=? 
{
=
1

~
-1

~
2

~
0

}

60049 name: Agar \( f(x)=(5x^2-7x+1)^5 \) bo'lsa f'(1)=?

::Agar \\( f(x)\=(5x^2-7x+1)^5 \\) bo'lsa f'(1)\=?::[html]
Agar \\( f(x)\=(5x^2-7x+1)^5 \\) bo'lsa f'(1)\=?
{
=
15

~
3

~
8

~
0

}

60048 name: Agar \( f(x)=x^2-8 \sqrt[]{x}+x \sqrt[]{x} \) bo'lsa f'(4)=?

::Agar \\( f(x)\=x^2-8 \\sqrt[]\{x\}+x \\sqrt[]\{x\} \\) bo'lsa f'(4)\=?::[html]
Agar \\( f(x)\=x^2-8 \\sqrt[]\{x\}+x \\sqrt[]\{x\} \\)   bo'lsa f'(4)\=?
{
=
9

~
2

~
-3

~
-2

}

60041 name: Funksiya hosilasini toping

::Funksiya hosilasini toping::[html]
Funksiya hosilasini toping \\( y\=x+\\sqrt\{x\}+\\sqrt[3]\{x\} \\)
{
=
\\( 1+\\frac\{1\}\{2\\sqrt\{x\}\}+\\frac\{1\}\{3\\sqrt\{x^2\}\} (x>0) \\)

~
\\( x+\\sqrt\{x\}+\\sqrt[3]\{x\} \\)

~
\\( - \\frac\{1\}\{1+x^2\} \\)

~
1+2sinx

}

60047 name: \( f(x)=x+ \frac{1}{x}+ \frac{1}{x^2} \) funksiya uchun f'(-1) ni hisoblang?

::\\( f(x)\=x+ \\frac\{1\}\{x\}+ \\frac\{1\}\{x^2\} \\) funksiya uchun f'(-1) ni hisoblang?::[html]
\\( f(x)\=x+ \\frac\{1\}\{x\}+ \\frac\{1\}\{x^2\} \\) funksiya uchun f'(-1) ni hisoblang? 
{
=
2

~
3

~
5

~
0

}

0 name: Switch category to $module$/top/По умолчанию для Joriy nazorat

$CATEGORY: $module$/top/По умолчанию для Joriy nazorat

60054 name: y=2sinx+cos2x funksiya y''=?

::y\=2sinx+cos2x funksiya y''\=?::[html]
y\=2sinx+cos2x  funksiya y''\=?
{
=
-2sinx-4cos2x

~
2cosx(1-2sinx)

~
\\( \\frac\{x^2-1\}\{x^2\} \\)

~
\\( \\frac\{x^3\}\{x^2-2x-1\} \\)

}

60057 name: y=arcctgx y(n) =?

::y\=arcctgx y(n) \=?::[html]
y\=arcctgx   y⁽ⁿ⁾  \=?       
{
=
\\( (cosy)^nsin( \\frac\{n \\pi \}\{2\}+ny ) \\)

~
\\( sin( \\frac\{n \\pi \}\{2\}+ny ) \\)

~
\\( cosy sin( \\frac\{ \\pi \}\{2\}+y ) \\)

~
\\( (cosy)^2 sin( \\frac\{2 \\pi \}\{2\}+2y ) \\)

}

60052 name: y=ax \( (a>0, a \neq 1 ) \) bo'lsin \( y^{(n)}=? \)

::y\=ax \\( (a>0, a \\neq 1 ) \\) bo'lsin \\( y^\{(n)\}\=? \\)::[html]
y\=a^x \\( (a>0, a \\neq 1 ) \\)  bo'lsin  \\( y^\{(n)\}\=? \\)
{
=
a^x lna

~
a^x ln²a

~
a^x ln³a

~
a^x lnⁿa

}

60053 name: y=sinx bo'lsin \( y^{(n)}=? \)

::y\=sinx bo'lsin \\( y^\{(n)\}\=? \\)::[html]
y\=sinx bo'lsin  \\( y^\{(n)\}\=? \\)
{
=
\\( sin(x+ \\frac\{ \\pi \}\{2\} ) \\)

~
\\( sin(x+ 2\\frac\{ \\pi \}\{2\} ) \\)

~
\\( sin(x+ 3\\frac\{ \\pi \}\{2\} ) \\)

~
\\( sin(x+ n\\pi \\frac\{ \\pi \}\{2\} ) \\)

}

60056 name: y=xm y(n) =?

::y\=xm y(n) \=?::[html]
y\=x^m   y⁽ⁿ⁾ \=?
{
=
\\( m(m-1)(m-2)...(m-(n-1)) x^\{(m-n)\} \\)

~
\\( \\frac\{(-1)^\{(n-1)\}(n-1)!\}\{x^n\} \\)

~
\\( sin(n \\frac\{ \\pi \}\{2\}+x ) \\)

~
\\( a^x(lna)^n \\)

}

60055 name: \( y=sinx+x^3 \) y=f(x) ning 2-tartibla hosilasi

::\\( y\=sinx+x^3 \\) y\=f(x) ning 2-tartibla hosilasi::[html]
\\( y\=sinx+x^3 \\)  y\=f(x) ning 2-tartibla hosilasi 
{
=
-sinx+6x

~
-cosx+6

~
sinx

~
cosx

}

60051 name: \( y=x^ \mu \) (x>0) bo'lsin. y'''=?

::\\( y\=x^ \\mu \\) (x>0) bo'lsin. y'''\=?::[html]
\\( y\=x^ \\mu \\) (x>0) bo'lsin. y'''\=?
{
=
\\( \\mu( \\mu-1 )( \\mu-2 )x^\{ \\mu-3 \} \\)

~
\\( \\mu( \\mu-1 )x^\{ \\mu-2 \} \\)

~
\\( \\mu x^\{ \\mu-1 \} \\)

~
\\( ( \\mu-n+1 )x^\{ \\mu-n \} \\)

}

0 name: Switch category to $module$/top/По умолчанию для Boshlang‘ich funksiya va aniqmas integral.

$CATEGORY: $module$/top/По умолчанию для Boshlang‘ich funksiya va aniqmas integral.

62899 name: Hisoblang

::Hisoblang::[html]
Hisoblang  \\( f(x)\=- \\frac\{x\}\{ \\sqrt[]\{1-x^2\} \} \\)
{
~
ln(kx+b) +C

~
cos(kx+b)+c

~
\\( \\frac\{x^3\}\{3\}+C \\)

=
\\( \\sqrt[]\{1-x^2\} +C \\)

}

62896 name: Kasrni integrallang

::Kasrni integrallang::[html]
Kasrni integrallang \\( \\int \\frac\{dx\}\{x^2+6x+10\} \\)
{
=
\\( arctg(x+3)+C \\)

~
\\( \\frac\{1\}\{6\}arctg(x+3)+C \\)

~
\\( ln|x+3\\lvert^2+C \\)

~
\\( \\frac\{1\}\{4\}arctg \\frac\{(x+3)\}\{2\} +C \\)

}

62895 name: quyidagi integralini toping

::quyidagi integralini toping::[html]
\\( \\int xdx \\) quyidagi integralini toping
{
=
\\( \\frac\{x^2\}\{2\} \\)

~
x+2

~
2x

~
0

}

62900 name: Quyidagi integralini toping
::Quyidagi integralini toping::[html]
Quyidagi\nintegralini toping \\( \\int \\frac\{1\}\{1+x^2\}dx \\)
{
=
\\( arctgx+C \\)

~
\\( arcsinx+C \\)

~
ln(kx+b) +C

~
cos(kx+b)

}

62901 name: Quyidagi integralini toping

::Quyidagi integralini toping::[html]
Quyidagi\nintegralini toping \\( \\int a^xdx \\)
{
=
\\( \\frac\{a^x\}\{ln a\}+C \\)

~
arctgx+C

~
ln(kx+b) +C

~
cos(kx+b)

}

62902 name: Quyidagi integralini toping

::Quyidagi integralini toping::[html]
 Quyidagi\nintegralini toping  \\( \\int \\frac\{1\}\{sin^2x\}dx \\)
{
=
\\( -ctgx+C \\)

~
tgx+C

~
ln(kx+b) +C

~
cos(kx+b)

}

62903 name: Quyidagi integralini toping

::Quyidagi integralini toping::[html]
Quyidagi integralini toping \\( \\int 1\\cdot dx \\)
{
=\\( x+c \\)
~
\\( x^2+c \\)

~
\\( x^3+c \\)

~
\\( x_2+c \\)

}

62904 name: Quyidagi integralini toping
::Quyidagi integralini toping::[html]
Quyidagi\nintegralini toping  \\( \\int2^x dx \\)
{
=
\\( \\frac\{2^x\}\{ln2\} \\)

~
sin(kx+b)

~
ln(kx+b) +C

~
cos(kx+b)

}

62898 name: Ushbu funksiyaning boshlang’ichini toping.

::Ushbu funksiyaning boshlang’ichini toping.::[html]
Ushbu funksiyaning \nboshlang’ichini toping. \\( \\frac\{1\}\{x\} , x>0 \\)
{
=
lnx+c

~
sin(kx+b)+c

~
ln(kx+b) +C

~
cos(kx+b)+c

}

62897 name: Ushbu funksiyaning boshlang’ichini toping. sin(kx+b),

::Ushbu funksiyaning boshlang’ichini toping. sin(kx+b),::[html]
Ushbu funksiyaning \nboshlang’ichini toping.  sin(kx+b),\n
{
=
cos(kx+b)

~
sin(kx+b)

~
ln(kx+b) +C

~
cos(kx+b)

}

0 name: Switch category to $module$/top/По умолчанию для Ratsional funksiyalarni integrallash.

$CATEGORY: $module$/top/По умолчанию для Ratsional funksiyalarni integrallash.

63276 name: Hisoblang

::Hisoblang::[html]
Hisoblang \\( \\int sin^3xdx \\)
{
=
\\( \\frac\{1\}\{3\}cos^3x-cosx+C \\)

~
\\( cosx+ \\frac\{1\}\{3\} cos^3x+C \\)

~
\\( sinx-\\frac\{1\}\{3\} cos^3x+C \\)

~
\\( \\frac\{1\}\{3\}cos^3x+sinx+C \\)

}

63277 name: Hisoblang

::Hisoblang::[html]
Hisoblang \\( \\int cos^2xdx \\)
{
=
\\( \\frac\{x\}\{2\}+ \\frac\{sin2x\}\{4\}+C \\)

~
\\( x+ \\frac\{1\}\{3\}cos^3x+C \\)

~
\\( sin x+ \\frac\{1\}\{3\}cos^3x+C \\)

~
\\( cosx+ \\frac\{1\}\{3\}cos^3x+C \\)

}

63278 name: Hisoblang

::Hisoblang::[html]
Hisoblang \\( \\int \\frac\{cosxdx\}\{sin^3x\} \\)
{
=
\\( - \\frac\{1\}\{2sin^2x\}+C \\)

~
\\( \\frac\{1\}\{2sin^2x\}+C \\)

~
\\( \\frac\{cosx\}\{sin^2x\}+C \\)

~
\\( \\frac\{1\}\{cos^2x\}+C \\)

}

63279 name: Hisoblang

::Hisoblang::[html]
\\( \\int \\frac\{dx\}\{\\sqrt\{x\}-\\sqrt[3]\{x\}\} \\)
{
=
\\( 2 \\sqrt[]\{x\}+3 \\sqrt[3]\{x\}+6ln( \\sqrt[6]\{x\}-1)+6 \\sqrt[6]\{x\} +C \\)

~
\\( 2 \\sqrt[]\{x\}+3 \\sqrt[3]\{x\}+6x+C \\)

~
\\( 2 \\sqrt[]\{x\}+3 \\sqrt[3]\{x\}+6 \\sqrt[6]\{x\} +C \\)

~
\\( 2 \\sqrt[]\{x\}-3 \\sqrt[3]\{x\}+C \\)

}

63280 name: Hisoblang

::Hisoblang::[html]
\\( \\int \\frac\{(1-x)dx\}\{\\sqrt[3]\{x^2\}\} \\)
{
=
\\( \\frac\{3\}\{4\}(4-x) \\sqrt[3]\{x\}+C \\)

~
\\( \\frac\{3\}\{4\}(x-4) \\sqrt[3]\{x\}+C \\)

~
\\( \\sqrt[]\{x\} - \\frac\{x^2\}\{2\}+C \\)

~
\\( \\sqrt[]\{x\}(4-x)+C \\)

}

63274 name: Ratsional kasrni integrallang

::Ratsional kasrni integrallang::[html]
Ratsional kasrni integrallang \\( \\int\\frac\{dx\}\{x^2+4x+7\} \\)
{
=
\\( \\int \\frac\{1\}\{\\sqrt\{3\}\}arctg\\frac\{x+2\}\{\\sqrt\{3\}\}+C \\)

~
\\( \\int \{\\sqrt\{3\}\}arctg\\frac\{x+2\}\{\\sqrt\{3\}\}+C \\)

~
\\( \\int arctg\\frac\{x+2\}\{\\sqrt\{3\}\}+C \\)

~
\\( \\int \\frac\{1\}\{2\}arctg\\frac\{x+2\}\{\\sqrt\{3\}\}+C \\)

}

63275 name: Ratsional kasrni integrallang

::Ratsional kasrni integrallang::[html]
Ratsional kasrni integrallang \\( \\int\\frac\{dx\}\{x^2+2x+2\} \\)
{
=
\\( arctg(x+1)+C \\)

~
\\( \\frac\{1\}\{2\} arctg \\frac\{(x+1)\}\{2\} +C \\)

~
\\( arctg(x+2)+C \\)

~
\\( \\( arctg(x+3)+C \\) \\)

}

62905 name: Ratsional kasrni integrallang

::Ratsional kasrni integrallang::[html]
Ratsional kasrni integrallang \\( \\int \\frac\{dx\}\{x^2+6x+10\} \\)
{
=
\\( arctg(x+3)+C \\)

~
\\( \\frac\{1\}\{6\}arctg(x+3)+C \\)

~
\\( ln \\left| \\begin\{matrix\} x+3\\end\{matrix\} \\right|^2+C \\)

~
\\( \\frac\{1\}\{4\}arctg \\frac\{x+3\}\{2\} +C \\)

}

0 name: Switch category to $module$/top/По умолчанию для Trigonometrik funksiyalarni integrallash.

$CATEGORY: $module$/top/По умолчанию для Trigonometrik funksiyalarni integrallash.

65255 name: Integrallang

::Integrallang::[html]
Integrallang \\( \\frac\{cosxdx\}\{sin^3x\} \\)
{
=
\\( - \\frac\{1\}\{2sin^2x\} +C \\)

~
\\( \\frac\{1\}\{2sin^2x+C\} \\)

~
\\( \\frac\{cosx\}\{sin^2x\} +C \\)

~
\\( \\frac\{1\}\{cos^2x\} +C \\)

}

65256 name: Integrallang

::Integrallang::[html]
Integrallang \\( \\int_\{\}^\{\}\{tg^2xdx\} \\)
{
=
tgx-x+C

~
\\( 2 \\sqrt[]\{x\} + 3\\sqrt[3]\{x\}+6x+C \\)

~
\\( 2 \\sqrt[]\{x\} + 3\\sqrt[3]\{x\}+6 \\sqrt[6]\{x\} +C \\)

~
\\( 2 \\sqrt[]\{x\} - 3\\sqrt[3]\{x\}+C \\)

}

65257 name: Integrallang

::Integrallang::[html]
Integrallang \\( \\int_\{\}^\{\}\{sin^4x cosxdx\} \\)
{
=
\\( \\frac\{1\}\{5\}sin^5x+C \\)

~
\\( ln \\left| \\begin\{matrix\} x^2+1 \\end\{matrix\} \\right| +C \\)

~
\\( ln \\left| \\begin\{matrix\} x+4\\end\{matrix\} \\right| +C \\)

~
\\( \\frac\{1\}\{2\} ln \\left| \\begin\{matrix\} x^2+2 \\end\{matrix\} \\right| +C \\)

}

65250 name: Kасрни интегралланг

::Kасрни интегралланг::[html]
Kасрни интегралланг  \\( \\int_\{\}^\{\}\{cos \\frac\{4\}\{3\}xcos3xdx \} \\)
{
=
\\( \\frac\{3\}\{26\} sin \\frac\{13\}\{3\}x+ \\frac\{3\}\{10\}sin \\frac\{5\}\{3\}x+C \\)

~
\\( \\frac\{1\}\{6\}arctg(x+3)+C \\)

~
\\( ln \\left| \\begin\{matrix\} x+3 \\end\{matrix\} \\right|^2+C \\)

~
\\( \\frac\{1\}\{4\}arctg \\frac\{(x+3)\}\{2\}+C \\)

}

65251 name: Kасрни интегралланг

::Kасрни интегралланг::[html]
Kасрни интегралланг \\( \\int_\{\}^\{\}\{sin3x\} \\cdot sin4xdx \\)
{
=
\\( \\frac\{1\}\{2\}sinx- \\frac\{1\}\{14\}sin7x+C \\)

~
\\( \\sqrt[]\{3\}arctg \\frac\{x+2\}\{ \\sqrt[]\{3\} \}+C \\)

~
\\( arctg \\frac\{x+2\}\{ \\sqrt[]\{3\} \}+C \\)

~
\\( \\frac\{1\}\{2\} arctg \\frac\{x+2\}\{ \\sqrt[]\{3\} \}+C \\)

}

65252 name: Kасрни интегралланг

::Kасрни интегралланг::[html]
Kасрни интегралланг \\( \\int_\{\}^\{\}\{sin^3x \\cdot cos^3x dx \} \\)
{
=
\\( \\frac\{1\}\{4\}sin^4x- \\frac\{1\}\{6\}sin^6x+C \\)

~
\\( \\frac\{1\}\{2\}arctg \\frac\{x+1\}\{2\}+C \\)

~
\\( arctg(x+2)+C \\)

~
\\( arctg(x+3)+C \\)

}

65253 name: Kасрни интегралланг

::Kасрни интегралланг::[html]
Kасрни интегралланг \\( \\int_\{\}^\{b\}\{sin^3xdx\} \\)
{
=
\\( \\frac\{1\}\{3\}cos^3x-cosx+C \\)

~
\\( sinx- \\frac\{1\}\{3\} cos^3x+C \\)

~
\\( cosx+\\frac\{1\}\{3\} cos^3x+C \\)

~
\\( \\frac\{1\}\{3\} cos^3x+sinx+C \\)

}

65254 name: Интегралланг

::Интегралланг::[html]
Интегралланг \\( \\int_\{\}^\{\}\{cos^2xdx\} \\)
{
=
\\( \\frac\{x\}\{2\}+ \\frac\{sin2x\}\{4\} +C \\)

~
\\( x+ \\frac\{1\}\{3\}cos^3x+C \\)

~
\\( sinx+ \\frac\{1\}\{3\}cos^3x+C \\)

~
\\( cosx+ \\frac\{1\}\{3\}cos^3x+C \\)

}

0 name: Switch category to $module$/top/По умолчанию для Xosmas integral tushunchasi. Integrallash sohasi chegaralanmagan xosmas integral.

$CATEGORY: $module$/top/По умолчанию для Xosmas integral tushunchasi. Integrallash sohasi chegaralanmagan xosmas integral.

66197 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{0\}^\{+ \\infty\} e^\{-x\}dx \\)
{
=
1

~
1,2

~
23

~
3,8

}

66198 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{a\}^\{+ \\infty\}\\frac\{dx\}\{x^a\} \\)  (a>0, \\( \\alpha \\)>0)
{
=
\\( \\frac\{a^\{1- \\alpha \}\}\{ \\alpha-1 \} \\)

~
\\( \\infty \\)

~
0

~
0,9

}

66199 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{0\}^\{+ \\infty\} cosxdx \\)
{
=
Mavjud emas

~
mavjud

~
7,8

~
8,005

}

66200 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{0\}^\{+ \\infty\}\\frac\{xlnx\}\{(1+x^2)^3\}dx \\)
{
=
-1/8

~
1,2

~
-23

~
3,8

}

66201 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{a\}^\{- \\infty\}\\frac\{dx\}\{x^2\} \\)  (a>0)
{
=
\\( \\frac\{1\}\{a\} \\)

~
a

~
-1

~
0

}

66202 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{-\\infty\}^\{+ \\infty\}\\frac\{dx\}\{1+x^2\} \\)
{
=
\\( \\pi \\)

~
4,5

~
0

~
\\( \\pi a^2 \\)

}

66203 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{-1\}^\{1\}\\frac\{dx\}\{\\sqrt\{1-x^2\}\} \\)
{
=
\\( \\pi \\)

~
\\( 3 \\pi \\)

~
\\( \\frac\{2 \\pi \}\{n+2\} \\)

~
\\( \\frac\{ \\pi a^2 \}\{2\} \\)

}

66204 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{2\}^\{+ \\infty\}\{ \\frac\{dx\}\{x^2+x-2\} \} \\)
{
=
\\( \\frac\{2\}\{3\}ln2 \\)

~
\\( \\frac\{ \\pi \}\{2\} \\)

~
\\( \\frac\{ 1 \}\{a\} \\)

~
\\( \\frac\{ 88 \}\{15\} \\)

}

66205 name: Hisoblang

::Hisoblang::[html]
\\( \\int_\{0\}^\{+\\infty\}\\frac\{dx\}\{1+x^3\} \\)
{
=
\\( \\frac\{2 \\pi \}\{3 \\sqrt[]\{3\} \} \\)

~
\\( \\pi /2-1\n \\)

~
1/5

~
3,8

}

0 name: Switch category to $module$/top/По умолчанию для Yuza tushunchasi. Kvadratlanuvchi soha.

$CATEGORY: $module$/top/По умолчанию для Yuza tushunchasi. Kvadratlanuvchi soha.

66242 name: 4y=8x-x2 va 4y=x+6 chiziqlar bilan chegaralangan shaklning yuzini toping

::4y\=8x-x2 va 4y\=x+6 chiziqlar bilan chegaralangan shaklning yuzini toping::[html]
4y\=8x-x²  va 4y\=x+6 chiziqlar bilan chegaralangan shaklning yuzini toping
{
=
\\( 5\\frac\{5\}\{24\} \\)

~
\\( \\frac\{205\}\{12\} \\)

~
\\( -\\frac\{95\}\{8\} \\)

~
\\( \\frac\{205\}\{12\} \\)

}

66248 name: Tekislikda ushbu \( \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 \) ellips bilan chegaralangan Q shaklning yuzi topilsin.

::Tekislikda ushbu \\( \\frac\{x^2\}\{a^2\}+ \\frac\{y^2\}\{b^2\}\=1 \\) ellips bilan chegaralangan Q shaklning yuzi topilsin.::[html]
Tekislikda ushbu \\( \\frac\{x^2\}\{a^2\}+ \\frac\{y^2\}\{b^2\}\=1 \\) ellips bilan chegaralangan Q shaklning yuzi topilsin.
{
=
\\( ab \\pi \\)

~
\\( \\pi \\)

~
\\( \\sqrt[]\{a^2-x^2\} \\)

~
\\( \\pi a^2 \\)

}

66243 name: \( (y-x)^2=x^3 \) , x=1 chiziqlar bilan chegaralangan shaklning yuzini toping

::\\( (y-x)^2\=x^3 \\) , x\=1 chiziqlar bilan chegaralangan shaklning yuzini toping::[html]
\\( (y-x)^2\=x^3 \\) , x\=1 chiziqlar bilan chegaralangan shaklning yuzini toping
{
=
\\( \\frac\{4\}\{5\} \\)

~
\\( + \\infty \\)

~
0

~
\\( \\frac\{5\}\{24\} \\)

}

66246 name: \( f(x)= \frac{a}{2}(e^{ \frac{x}{a} }+e^{- \frac{x}{a} }) \), \( 0 \leq x \leq a \), a>0 zanjir chiziqni Ox o'q atrofida aylantirishdan xosil bo'lgan aylanish sirtining yuzini toping.

::\\( f(x)\= \\frac\{a\}\{2\}(e^\{ \\frac\{x\}\{a\} \}+e^\{- \\frac\{x\}\{a\} \}) \\), \\( 0 \\leq x \\leq a \\), a>0 zanjir chiziqni Ox o'q atrofida aylantirishdan xosil bo'lgan aylanish sirtining yuzini toping.::[html]
\\( f(x)\= \\frac\{a\}\{2\}(e^\{ \\frac\{x\}\{a\} \}+e^\{- \\frac\{x\}\{a\} \}) \\), \\( 0 \\leq x \\leq a \\), a>0  zanjir chiziqni Ox o'q atrofida aylantirishdan xosil bo'lgan aylanish sirtining yuzini toping.
{
=
\\( \\frac\{ \\pi a^2 \}\{4\}(e^2-e^\{-2\}+4) \\)

~
\\( \\frac\{ \\pi a^2 \}\{4\} \\)

~
a/2

~
\\( \\frac\{ \\pi a\}\{2\} \\)

}

66247 name: \( x^2+(y-2)^2=1 \) aylanani Ox o'q atrofida aylantirishdan hosil bo'lgan aylanish sirtining (tor) yuzini toping.

::\\( x^2+(y-2)^2\=1 \\) aylanani Ox o'q atrofida aylantirishdan hosil bo'lgan aylanish sirtining (tor) yuzini toping.::[html]
\\( x^2+(y-2)^2\=1 \\) aylanani Ox o'q atrofida aylantirishdan hosil bo'lgan aylanish sirtining (tor) yuzini toping.
{
=
\\( 8 \\pi^2 \\)

~
\\( \\frac\{ \\pi a^2 \}\{4\}(e^2-e^\{-2\}+4) \\)

~
\\( e^\{ \\frac\{x\}\{a\} \} \\)

~
\\( e^\{-2\}+4 \\)

}

66249 name: \( \rho= \rho( \ominus )=a(1-cos \ominus ) (a \in R, 0 \leq \ominus \leq 2 \pi ) \)

::\\( \\rho\= \\rho( \\ominus )\=a(1-cos \\ominus ) (a \\in R, 0 \\leq \\ominus \\leq 2 \\pi ) \\)::[html]
\\( \\rho\= \\rho( \\ominus )\=a(1-cos \\ominus ) (a \\in R, 0 \\leq \\ominus \\leq 2 \\pi ) \\)
{
=
\\( \\frac\{3\}\{2\} \\pi a^2 \\)

~
3/2

~
\\( 2cos \\ominus \\)

~
\\( \\frac\{3\}\{2\} \\Theta \\)

}

66244 name: \( {x=asin^3t \brace y=bcos^3t} \) (\( 0 \leq t \leq2 \pi \)) chiziq bilan chegaralangan shaklning yuzini toping

::\\( \{x\=asin^3t \\brace y\=bcos^3t\} \\) (\\( 0 \\leq t \\leq2 \\pi \\)) chiziq bilan chegaralangan shaklning yuzini toping::[html]
\\( \{x\=asin^3t \\brace y\=bcos^3t\} \\) (\\( 0 \\leq t \\leq2 \\pi \\))  chiziq bilan chegaralangan shaklning yuzini toping
{
=
\\( \\frac\{3ab \\pi \}\{8\} \\)

~
4/5

~
95/8

~
0

}

66245 name: \rho=\frac{3acos\varphi sin\varphi}{sin^3\varphi+cos^3\varphi}

::\\rho\=\\frac\{3acos\\varphi sin\\varphi\}\{sin^3\\varphi+cos^3\\varphi\}::[html]
\\( \\rho\=\\frac\{3acos\\varphi sin\\varphi\}\{sin^3\\varphi+cos^3\\varphi\} \\)  Chiziq bilan chegaralangan shaklning yuzini toping
{
=
\\( \\frac\{3a^2\}\{2\} \\)

~
\\( 1+tg^3 \\phi \\)

~
\\( \\frac\{9a^2\}\{2\} \\)

~
\\( \\frac\{1\}\{3\} \\)

}

0 name: Switch category to $module$/top/По умолчанию для Aylanma sirt yuzasining ta’rifi va uning aniq integral yordamida ifodalanishi.

$CATEGORY: $module$/top/По умолчанию для Aylanma sirt yuzasining ta’rifi va uning aniq integral yordamida ifodalanishi.

68205 name: aylanishidan hosil bo`lgan sirt yuzalarini toping

::aylanishidan hosil bo`lgan sirt yuzalarini toping::[html]
\\( y\=acos \\frac\{ \\pi x \}\{2b\}( \\left| \\begin\{matrix\} x \\end\{matrix\} \\right| ) \\) OX o'qi atrofida aylanishidan hosil bo`lgan sirt\nyuzalarini toping
{
=
\\( 2a \\sqrt[]\{ \\pi^2a^2+4b^2 \} + \\frac\{8b^2\}\{ \\pi \}ln( \\frac\{ \\pi a \}\{2b\}+ \\frac\{ \\sqrt[]\{ \\pi^2a^2+4b^2 \} \}\{2b\} ) \\)

~
\\( \\frac\{91 \\pi \}\{3\} \\)

~
\\( \\frac\{61 \\pi \}\{5\} \\)

~
\\( \\frac\{5\}\{24\} \\)

}

68206 name: Ushbu x=a(t-sint), y=a(1-cost) \( (0 \leq t \leq 2 \pi ) \) OX o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping

::Ushbu x\=a(t-sint), y\=a(1-cost) \\( (0 \\leq t \\leq 2 \\pi ) \\) OX o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping::[html]
Ushbu  x\=a(t-sint), y\=a(1-cost) \\( (0 \\leq t \\leq 2 \\pi ) \\) OX o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping 
{
=
\\( \\frac\{64\}\{3\} \\pi a^2 \\)

~
\\( \\frac\{4\}\{15\} \\)

~
\\( \\frac\{3\}\{7\} \\pi ab^2 \\)

~
\\( \\frac\{16\}\{15\} \\pi \\)

}

68209 name: Ushbu \( y=tg x(0 \leq x \leq \frac{ \pi }{4} ) \) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping.

::Ushbu \\( y\=tg x(0 \\leq x \\leq \\frac\{ \\pi \}\{4\} ) \\) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping.::[html]
Ushbu \\( y\=tg x(0 \\leq x \\leq \\frac\{ \\pi \}\{4\} ) \\) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping.
{
=
\\( \\pi [( \\sqrt[]\{5\}- \\sqrt[]\{2\} )+ln \\frac\{( \\sqrt[]\{2\}+1)( \\sqrt[]\{5\}-1 )\}\{2\} ] \\)

~
\\( \\frac\{1\}\{3\}cos^3 t \\)

~
\\( \\frac\{3\}\{7\}cos^7t- \\frac\{1\}\{9\}cos^9t \\)

~
\\( a cos \\frac\{ \\pi x \}\{2b\} \\)

}

68207 name: \( x^{2/3}+y^{2/3}=a^{2/3} \) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping

::\\( x^\{2/3\}+y^\{2/3\}\=a^\{2/3\} \\) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping::[html]
\\( x^\{2/3\}+y^\{2/3\}\=a^\{2/3\} \\) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping
{
=
\\( \\frac\{12\}\{5\} \\pi a^2 \\)

~
\\( \\pi \\)

~
\\( \\sqrt[]\{a^2-x^2\} \\)

~
\\( \\pi a^2 \\)

}

68208 name: \( \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 \) \( (0< b \leq a ) \) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping

::\\( \\frac\{x^2\}\{a^2\}+ \\frac\{y^2\}\{b^2\}\=1 \\) \\( (0< b \\leq a ) \\) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping::[html]
\\( \\frac\{x^2\}\{a^2\}+ \\frac\{y^2\}\{b^2\}\=1 \\) \\( (0< b \\leq a ) \\) Ox o'qi atrofida aylanishidan hosil bo'lgan sirt yuzlarini toping
{
=
\\( 2 \\pi b^2+2 \\pi ab \\frac\{arcsin8\}\{8\} \\)

~
\\( \\frac\{ \\pi a^2\}\{4\} \\)

~
\\( \\frac\{a\}\{2\} \\)

~
\\( \\frac\{ \\pi a\}\{2\} \\)

}

0 name: Switch category to $module$/top/По умолчанию для Aniq integralning fizikaga tadbiqlari.

$CATEGORY: $module$/top/По умолчанию для Aniq integralning fizikaga tadbiqlari.

70343 name: . Ushbu formula bilan berilgan sohaning og’irlik markazining koordinatalarini toping.

::. Ushbu formula bilan berilgan sohaning og’irlik markazining koordinatalarini toping.::[html]
Ushbu  formula \\( \\frac\{x^2\}\{a^2\}+ \\frac\{y^2\}\{b^2\} \\leq 1 \\) bilan berilgan   sohaning og’irlik markazining\nkoordinatalarini toping. \\( (0 \\leq x \\leq a , 0 \\leq y \\leq b ) \\)
{
=
\\( ( \\frac\{4a\}\{3 \\pi \}; \\frac\{4b\}\{3 \\pi \} ) \\)

~
\\( (\\frac\{9a\}\{20 \}; \\frac\{9a\}\{20 \} ) \\)

~
\\( (0; \\frac\{3\}\{8\}a ) \\)

~
\\( ( \\frac\{9a\}\{20\}; \\frac\{4b\}\{3 \\pi \} ) \\)

}

70344 name: Agar 1 кгс kuch elastik prujinani 1 sm ga cho'zsa, bu prujinani 10 sm ga cho'zish uchun qancha ish qilish kerak?

::Agar 1 кгс kuch elastik prujinani 1 sm ga cho'zsa, bu prujinani 10 sm ga cho'zish uchun qancha ish qilish kerak?::[html]
Agar 1 кг/с kuch elastik prujinani 1 sm ga cho'zsa, bu prujinani 10 sm ga cho'zish uchun qancha ish qilish kerak?
{
=
0,5

~
0,39

~
0,6

~
0,7

}

70342 name: Asosi b ga balandligi h ga teng bo’lgan uchburchakli plastinkaning statik va inersiya momentini toping

::Asosi b ga balandligi h ga teng bo’lgan uchburchakli plastinkaning statik va inersiya momentini toping::[html]
Asosi b  ga  balandligi  \nh  ga  teng \nbo’lgan   uchburchakli plastinkaning  \\( \\rho\=1 \\) statik\nva inersiya momentini toping
{
=
\\( \\frac\{bh^2\}\{6\} \\);\\( \\frac\{bh^3\}\{12\} \\)

~
\\( \\frac\{ \\pi ab^2 \}\{4\} \\)

~
\\( \\frac\{bh^2\}\{6\} \\)

~
\\( b^2/9 \\)

}

70345 name: Nuqtaning tezligi qonuniyat bilan o’zgarsa u vaqt oralig'ida qanday yo'lni bosib o'tadi?

::Nuqtaning tezligi qonuniyat bilan o’zgarsa u vaqt oralig'ida qanday yo'lni bosib o'tadi?::[html]
Nuqtaning  tezligi \\( v\=v_0+at \\)qonuniyat bilan o’zgarsa u \\( [0,T] \\)vaqt oralig'ida qanday yo'lni bosib o'tadi?
{
=
\\( v_0T+ \\frac\{a\}\{2\}T^2 \\)

~\\( \\frac\{4\}\{15\} \\pi \\delta \\omega^2R^3 \\)

~
\\( mg \\frac\{Rh\}\{R+h\} \\)

~
\\( \\frac\{ \\gamma H^2 \}\{6E\} \\)

}

70341 name: Uzunligi l= 10 m bo'lgan, tayoqning chiziqli zichligi qonunga muvofiq o'zgarsa novda massasini aniqlang.Bu erda x – novda bir uchidan 2-uchigacha masofa

::Uzunligi l\= 10 m bo'lgan, tayoqning chiziqli zichligi qonunga muvofiq o'zgarsa novda massasini aniqlang.Bu erda x – novda bir uchidan 2-uchigacha masofa::[html]
Uzunligi l\= 10 m\nbo'lgan, tayoqning chiziqli\nzichligi \\( \\delta \=6+0.3x \\) кг/м qonunga muvofiq\no'zgarsa  novda massasini aniqlang.Bu\nerda x – novda bir  uchidan\n2-uchigacha  masofa 

{
=
75

~
45

~
67

~
42

}

0 name: Switch category to $module$/top/По умолчанию для Sonli qator tushunchasi, yaqinlashuvchi qator va uning yig'indisi.

$CATEGORY: $module$/top/По умолчанию для Sonli qator tushunchasi, yaqinlashuvchi qator va uning yig'indisi.

70346 name: 1+2+3+......+n+.... qator haqida nima deyish mumkin?

::1+2+3+......+n+.... qator haqida nima deyish mumkin?::[html]
1+2+3+......+n+.... qator haqida   nima  deyish   mumkin?
{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Funksional\nqator

}

70348 name: qator haqida nima deyish mumkin?

::qator haqida nima deyish mumkin?::[html]
\\( \\sum_\{m\=1\} ^\{\\infty\} aq^\{n-1\}, \\mid q\\mid>1 \\)  qator haqida   nima \ndeyish   mumkin?
{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

}

70347 name: Ushbu qator haqida nima deyish mumkin?

::Ushbu qator haqida nima deyish mumkin?::[html]
Ushbu \\( \\sum_\{m\=1\}^ \\infty (-1)^\{n+1\} \\) qator haqida  \nnima  deyish   mumkin?
{
=
 Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

}

70349 name: Ushbu , qator haqida nima deyish mumkin?

::Ushbu , qator haqida nima deyish mumkin?::[html]
Ushbu \\( \\sum_\{n\=1\}^\{ \\infty \} \\frac\{1\}\{ \\sqrt[]\{n\}\}\\)\\(\\mid q \\mid>1 \\) qator haqida  nima \ndeyish   mumkin?
{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

}

70350 name: Ushbu qator haqida nima deyish mumkin?

::Ushbu qator haqida nima deyish mumkin?::[html]
Ushbu qator haqida   nima \ndeyish   mumkin? \\( \\sum_\{n\=1\}^ \\infty \\frac\{sin n\}\{2^n\} \\)
{
=
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

~
Uzoqlashuvchi

}

0 name: Switch category to $module$/top/По умолчанию для Taqqoslash teoremalari. Koshi va Dalamber alomatlari.

$CATEGORY: $module$/top/По умолчанию для Taqqoslash teoremalari. Koshi va Dalamber alomatlari.

72506 name: qator haqida nima deyish mumkin?

::qator haqida nima deyish mumkin?::[html]
\\( \\sum_\{n\=2\}^\\infty \\frac\{ln^3 n\}\{n^2\} \\)
{
=
Yaqinlashuvchi

~
Uzoqlashuvchi

~
Musbat qator

~
Ishorasi almashinuvchi \nqator

}

72507 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( \\sum_\{n\=3\}^\\infty \\frac\{1\}\{(ln)^\{lnln n\}\} \\)
{
=
Yaqinlashuvchi

~
Uzoqlashuvchi

~
Musbat qator

~
Funksional qator

}

72508 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( \\sum_\{n\=3\}^\\infty (\\frac\{n+1\}\{n+2\})^\{n^\{2\}\} \\)
{
=
Yaqinlashuvchi

~
Uzoqlashuvchi

~
Musbat\nqator

~
Funksional\nqator

}

72509 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( \\sum_\{n\=1\}^\\infty \\frac\{n!\}\{n^n\} \\)
{
=
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

~
Uzoqlashuvchi

}

72510 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( 1 \\frac\{1\}\{2\} -\\frac\{1\}\{3\} + \\frac\{1\}\{4\}+ \\frac\{1\}\{5\} - \\frac\{1\}\{6\}+.... \\)
{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Ishorasi almashinuvchi \nqator

}

0 name: Switch category to $module$/top/По умолчанию для Ishora navbatlashuvchi qatorlar. Leybnits teoremasi.

$CATEGORY: $module$/top/По умолчанию для Ishora navbatlashuvchi qatorlar. Leybnits teoremasi.

72514 name: Ushbu qator qanday qator?

::Ushbu qator qanday qator?::[html]
\\( 1- \\frac\{1\}\{2\}+ \\frac\{1\}\{3\}- \\frac\{1\}\{4\}+...+(-1)^\{n-1\} \\frac\{1\}\{n\}+ \\)
{
=
Ishoralari  almashinuvchi \n

~
Absolyut  Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

}

72511 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( 1+ \\frac\{1\}\{2\} - \\frac\{1\}\{3\}+ \\frac\{1\}\{4\}+ \\frac\{1\}\{5\}- \\frac\{1\}\{6\}+.... \\)
{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Ishorasi almashinuvchi \nqator

}

72512 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( \\sum_\{n\=1\}^\\infty \\frac\{1\}\{ \\sqrt[]\{n(n+1)\} \} \\)
{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Ishorasi almashinuvchi \nqator

}

72513 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( 1- \\frac\{1\}\{2\}+ \\frac\{1\}\{3\}- \\frac\{1\}\{4\}+...+(-1)^\{n-1\} \\frac\{1\}\{n\}+ \\)
{
=
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

~
Uzoqlashuvchi

}

72515 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( 1+ \\frac\{1\}\{2\}+ \\frac\{1\}\{3\}+ \\frac\{1\}\{4\}+...+ \\frac\{1\}\{n\}+ \\)
{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

}

0 name: Switch category to $module$/top/По умолчанию для Absolyut va shartli yaqinlashuvchi qatorlar.

$CATEGORY: $module$/top/По умолчанию для Absolyut va shartli yaqinlashuvchi qatorlar.

72516 name: qator haqida nima deyish mumkin?

::qator haqida nima deyish mumkin?::[html]
\\( \\sum_\{n\=1\}^\\infty (-1)^\{n+1\}\=1-1+1-1+..... \\) qator  haqida \nnima  deyish mumkin?

{
=
Uzoqlashuvchi

~
Yaqinlashuvchi

~
Musbat qator

~
Ishorasi almashinuvchi \nqator

}

72517 name: Ushbu qator yig’indisini toping

::Ushbu qator yig’indisini toping::[html]
\\( \\sum_\{n\=1\}^\\infty \\frac\{3\}\{9n^2-3n-2\} \\)
{
=
1

~
0

~
-1

~
\\( \\infty \\)

}

72518 name: Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?

::Ushbu qatorni yaqinlahuvchilikka tekshirsak nima bo’ladi?::[html]
\\( \\sum_\{n\=2\}^\\infty \\frac\{1\}\{(n+5)ln^2 (n+1)\} \\)
{
=
Yaqinlashuvchi

~
Musbat qator

~
Funksional qator

}

72519 name: Ushbu qatorning yig’indisini toping?

::Ushbu qatorning yig’indisini toping?::[html]
\\( \\lim_\{n \\rightarrow \\infty\} \\frac\{(2n-1)!!\}\{n^n\} \\)
{
=
Yaqinlashuvchi

~
Musbat qator

~
Uzoqlashuvchi

~
Ishorasi almashinuvchi \nqator

}

0 name: Switch category to $module$/top/По умолчанию для Funksional ketma-ketlik tushunchasi. Yaqinlashuvchi ketma-ketlik, uning limiti.

$CATEGORY: $module$/top/По умолчанию для Funksional ketma-ketlik tushunchasi. Yaqinlashuvchi ketma-ketlik, uning limiti.

73130 name: funksional qator haqida nima deyish mumkin?

::funksional qator haqida nima deyish mumkin?::[html]
\\sum_\{k\=1\}^\\infty (x^\{\\frac\{1\}\{2n+1\}\}-x^\{\\frac\{1\}\{2n-1\}\})    \\( 0 \\leq x \\leq 1 \\) 
funksional\nqator haqida  nima  deyish mumkin?
{
=
Tekis  Yaqinlashmaydi

~
Musbat qator

~
Uzoqlashuvchi

~
Ishorasi almashinuvchi \nqator

}

73128 name: Nuqtalar o’rniga mos so’zni tanlang. Agar funksional qatorning qismiy yig`indilaridan tuzilgan Snxfunksional ketma-ketlik M to`plamda qatorning yig`indisi Sxga tekis yaqinlashsa, unda funksional qator M to`plamda ……..deyiladi qator haqida nim

::Nuqtalar o’rniga mos so’zni tanlang. Agar funksional qatorning qismiy yig`indilaridan tuzilgan Snxfunksional ketma-ketlik M to`plamda qatorning yig`indisi Sxga tekis yaqinlashsa, unda funksional qator M to`plamda ……..deyiladi qator haqida nim::[html]

\n
1. Nuqtalar o’rniga  mos \n so’zni tanlang.
\n

\n\n
Agar funksional\nqatorning qismiy yig`indilaridan tuzilgan \n\{Sn(x)\} funksional ketma-ketlik M to`plamda qatorning\nyig`indisi S(x) ga tekis yaqinlashsa, unda funksional qator M to`plamda ……..deyiladi
\n\n
{
=