Ekstremumning yetarli shartlaridan foydalanib, 𝑧 = 2𝑦 − 𝑥2 − 𝑦2 funksiyani ekstremumga tekshiring. Используя достаточные условия экстремума, функция двух переменных, исследуйте на экстремум функцию 𝑧 = 2𝑦 − 𝑥2 − 𝑦2. Check function 𝑧 = 2𝑦 − 𝑥2 − 𝑦2 for an extremum using the sufficient conditions of extremum.

funktsiya (0,1) nuqtada maksimumga erishadi/функция достигает максимум в точке (0, 1)/ function reaches a maximum at point (0,1)

ekstremumga ega emas /не имеет экстремума/ has no extremum

funktsiya (0,1) nuqtada minimumga erishadi/функция достигает минимума в точке (0, 1)/ function reaches a minimum at point (0,1).

85. Funksiya ekstremumi ta’rifidan foydalanib, 𝑧 = (𝑥 − 2)4 + (𝑦 − 3)4 funksiyaning (2,3) nuqtada ekstremumga tekshiring. Пользуясь определением экстремума функции, исследуйте на экстремум функцию 𝑧 = (𝑥 − 2)4 + (𝑦 − 3)4 в точке (2,3). Using the definition of an extremum of a function, verify function 𝑧 = (𝑥 − 2)4 + (𝑦 − 3)4 to extremum at point (2,3).

funksiya maksimumga erishadi/ функция достигает максимума/function has maximum

funksiya minimumga erishadi/ функция достигает минимума/

maksimumi yo’q/ нет максимума/ no maximum

Funksiya ekstremumi ta’rifidan foydalanib, (2,3) nuqtada 𝑧 = 1 − (𝑥 − 2)4 − (𝑦 − 3)4 funksiyani ekstremumga tekshiring. Пользуясь определением экстремума функции, исследуйте на экстремум функцию 𝑧 = 1 − (𝑥 − 2)4 − (𝑦 − 3)4 в точке (2,3). Using the definition of an extremum of a function, verify function 𝑧 = 1 − (𝑥 − 2)4 − (𝑦 − 3)4 to extremum of at point (2,3).

funksiya maksimumga erishadi/ функция достигает максимума/function has maximum

funksiya minimumga erishadi/ функция достигает минимума/= function has minimum

maksimumi yo’q/ нет максимума/ no maximum

minimum yo’q/нет минимума/= no minimum

𝑥2 − 𝑦2 = 𝑎2 oshkormas funksiya berilgan 𝛛𝑦 𝛛𝑥 ni toping. Найдите 𝑑𝑦 𝑑𝑥 неявной функции 𝑥2 − 𝑦2 = 𝑎2. Find 𝛛𝑦 𝛛𝑥 of implict function 𝑥2 − 𝑦2 = 𝑎2.

𝑑𝑦 = − 𝑥 𝑑𝑥 𝑦

𝑑𝑦 = − 𝑥 𝑑𝑥 2𝑦

82. 𝑥2 + 𝑦2 = 𝑎2 oshkormas funksiya berilgan, 𝛛 𝛛𝑥 ni toping. Найдите 𝑑𝑦 𝑑𝑥 неявной функции 𝑥2 + 𝑦2 = 𝑎2. Find 𝛛𝑦 𝛛𝑥 of implict function 𝑥2 + 𝑦2 = 𝑎2.

𝑑𝑦 = − 𝑥 𝑑𝑥 𝑦

𝑑𝑦 = − 𝑥 𝑑𝑥 2𝑦

𝑧 = ln(𝑥2 − 𝑦2) funksiya berilgan, 𝛛𝑧 𝛛𝑦 ni toping. Найдите 𝛛𝑧 𝛛𝑦 функции 𝑧 = ln(𝑥2 − 𝑦2). Find 𝛛𝑧 𝛛𝑦 of the function = ln(𝑥2 − 𝑦2) .

𝛛𝑧 = − 2𝑦 𝛛𝑦 𝑥2−𝑦2

𝛛𝑧 = 2𝑦 𝛛𝑦 𝑥2−𝑦2

𝛛𝑧 = − 2𝑦 𝛛𝑦 𝑥2−𝑦2

𝛛𝑧 = − 𝑦 𝛛𝑦 𝑥2−𝑦2

79. 𝑧 = ln(𝑥2 − 𝑦2) funksiya berilgan, 𝛛𝑧 𝛛𝑥 ni toping. Найдите 𝛛𝑧 𝛛𝑥 функции 𝑧 = ln(𝑥2 − 𝑦2) . Find 𝛛𝑧 𝛛𝑥 of the function = ln(𝑥2 − 𝑦2) .

𝛛𝑧 = 2𝑥 𝛛𝑥 𝑥2−𝑦2

𝛛𝑧 = − 2𝑥 𝛛𝑥 𝑥2−𝑦2

𝛛𝑧 = 𝑥 𝛛𝑥 𝑥2−𝑦2

78. Agar 𝑧 = 2 bo’lsa, d𝑧 ni toping, 𝑥 = 𝑒𝑡, 𝑦 = 1 − 𝑒2𝑡. Найдите d𝑧 если 𝑧 = 2, 𝑥 d𝑡 d𝑡 𝑥 где 𝑥 = 𝑒𝑡, 𝑦 = 1 − 𝑒2𝑡. Find d𝑧 d𝑡 if 𝑧 = 2, where 𝑥 = 𝑒𝑡, 𝑦 = 1 − 𝑒2𝑡.

𝑑𝑧 = − 2 𝑒𝑡 𝑑𝑡

𝑑𝑧 = 2 𝑥2 𝑒𝑡 𝑑𝑡 𝑥2

𝑑𝑧 = − 3 𝑒𝑡 𝑑𝑡 𝑥2

𝑑𝑧 = − 4 𝑒𝑡 𝑑𝑡 𝑥2

𝑧 = 𝑥2 + 𝑥𝑦 + 𝑦2 murakkab funksiyaning hosilasini toping, 𝑥 = 𝑡2, 𝑦 = 𝑡. Найдите производную сложной функции 𝑧 = 𝑥2 + 𝑥𝑦 + 𝑦2, где 𝑥 = 𝑡2, 𝑦 = 𝑡. Find the derivative of composite function 𝑧 = 𝑥2 + 𝑥𝑦 + 𝑦2, where 𝑥 = 𝑡2, 𝑦 = 𝑡.

𝑑𝑧 = 2(2𝑥 + 𝑦)𝑡 + (𝑥 + 2𝑦) 𝑑𝑡

𝑑𝑧 = (2𝑥 + 𝑦)𝑡 + (𝑥 + 2𝑦) 𝑑𝑡

𝑑𝑧 = 2(2𝑥 + 𝑦)𝑡 + 2(𝑥 + 2𝑦) 𝑑𝑡

𝑑𝑧 = (2𝑥 + 𝑦)𝑡 − (𝑥 + 2𝑦) 𝑑𝑡

76. 𝑢 = 𝑥3 + 𝑦4 + 5 funksiya berilgan, 𝛛3𝑢 𝛛𝑥2 𝛛𝑦 ni toping. Найти 𝛛3𝑢 𝛛𝑥2 𝛛𝑦 функции 𝑢 = 𝑥3 + 𝑦4 + 5. Find 𝛛3𝑢 𝛛𝑥2 𝛛𝑦 of function 𝑢 = 𝑥3 + 𝑦4 + 5.

𝛛3𝑢 = 0 𝛛𝑥2 𝛛𝑦

𝛛3𝑢 = 1 𝛛𝑥2 𝛛𝑦

𝛛3𝑢 = 2 𝛛𝑥2 𝛛𝑦

𝛛3𝑢 = 3 𝛛𝑥2 𝛛𝑦

74. 𝑢 = 𝑥𝑦 + 10 funksiya berilgan, 𝛛3𝑢 𝛛𝑥2 𝛛𝑦 ni toping. Найти 𝛛3𝑢 𝛛𝑥2 𝛛𝑦 функции 𝑢 = 𝑥𝑦 + 10. Find 𝛛3𝑢 𝛛𝑥2 𝛛𝑦 of function 𝑢 = 𝑥𝑦 + 10.

𝛛3𝑢 = 0 𝛛𝑥2 𝛛𝑦

𝛛3𝑢 = 1 𝛛𝑥2 𝛛𝑦

𝛛3𝑢 = 2 𝛛𝑥2 𝛛𝑦

𝛛3𝑢 = 3 𝛛𝑥2 𝛛𝑦

𝑢 = cos(𝑥 − 𝑦) funksiya berilgan, 𝛛3𝑢 𝛛𝑥2𝛛𝑦 ni toping Найти 𝛛3𝑢 𝛛𝑥2 𝛛𝑦 функции 𝑢 = cos(𝑥 − 𝑦). Find 𝛛3𝑢 𝛛𝑥2𝛛𝑦 of function 𝑢 = cos(𝑥 − 𝑦).

𝛛3𝑢 𝛛𝑥2 𝛛𝑦 = −sin(𝑥 − 𝑦)

𝛛3𝑢 𝛛𝑥2 𝛛𝑦 sin(𝑥 − 𝑦)

𝛛3𝑢 𝛛𝑥2 𝛛𝑦 −sin(𝑥 + 𝑦)

𝛛3𝑢 𝛛𝑥2 𝛛𝑦−2sin(𝑥 − 𝑦)

𝑧 = 𝑥3 + 𝑦2 funksiyaning ikkinchi tartibli xususiy hosilasini 𝛛2𝑧 𝛛𝑥2 toping. Найдите частную производную второго порядка 𝛛2𝑧 𝛛𝑥2 функции 𝑧 = 𝑥3 + 𝑦2. Find the second order partial derivative 𝛛2𝑧 𝛛𝑥2 of the function 𝑧 = 𝑥3 + 𝑦2.

𝛛2𝑧 = −6𝑥 𝛛𝑥 2

𝑧 = x𝑦 funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = x𝑦. Find total differential of the function 𝑧 = 𝑥𝑦.

𝑑𝑧 = 𝑦𝑑𝑥 + 𝑥𝑑𝑦

𝑑𝑧 = 𝑦𝑑𝑥 − 𝑥𝑑𝑦

𝑑𝑧 = 𝑦𝑑𝑥 + 2𝑥𝑑𝑦

𝑑𝑧 = −𝑦𝑑𝑥 + 𝑥𝑑𝑦

67. 𝑧 = 𝑒𝑥2−𝑦2 funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = 𝑒𝑥2−𝑦2 . Find total differential of function 𝑧 = 𝑒𝑥2−𝑦2 .

𝑑𝑧 = 2𝑥𝑒𝑥2−𝑦2 𝑑𝑥 − 2𝑦𝑒𝑥2−𝑦2 𝑑𝑦

𝑑𝑧 = 2𝑥𝑒𝑥2−𝑦2 𝑑𝑥 − 𝑦𝑒𝑥2−𝑦2 𝑑𝑦

𝑑𝑧 = 𝑥𝑒𝑥2−𝑦2 𝑑𝑥 − 2𝑦𝑒𝑥2−𝑦2 𝑑𝑦

𝑑𝑧 = 𝑥𝑒𝑥2−𝑦2 𝑑𝑥 − 𝑦𝑒𝑥2−𝑦2 𝑑𝑦

66. 𝑢 = √𝑥2 − 𝑦2 funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑢 = √𝑥2 − 𝑦2. Find total differential of the function 𝑢 = √𝑥2 − 𝑦2.

𝑑𝑢 = 𝑥 √𝑥2+𝑦2 d𝑥 − 𝑦 √𝑥2+𝑦2 𝑑𝑦

𝑑𝑢 = 𝑥 √𝑥2+𝑦2 d𝑥 − 𝑦 √𝑥2+𝑦2 𝑑𝑦 √𝑥2+𝑦2

𝑑𝑢 = 𝑥 √𝑥2+𝑦2 d𝑥 + 𝑦 √𝑥2+𝑦2 𝑑𝑦

𝑑𝑢 = − 𝑥 d𝑥 − 𝑦 𝑑𝑦 √𝑥2+𝑦2

65. 𝑢 = √𝑥2 + 𝑦2 funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑢 = √𝑥2 + 𝑦2. Find total differential of the function 𝑢 = √𝑥2 + 𝑦2

𝑑𝑢 = 𝑥 √𝑥2+𝑦2 d𝑥 + 𝑦 √𝑥2+𝑦2 𝑑𝑦 √𝑥2+𝑦2 = 𝑑𝑢 = − 𝑥

𝑑𝑢 = 𝑥 √𝑥2+𝑦2 d𝑥 − 𝑦 𝑑𝑦 √𝑥2+𝑦2

𝑑𝑢 = − 𝑥√𝑥2+𝑦2 𝑑𝑦 √𝑥2+𝑦2 d𝑥 − 𝑦

d𝑥 + 𝑦√𝑥2+𝑦2 𝑑 𝑦

𝑧 = 𝑥2𝑦2funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = 𝑥2𝑦2. Find total differential of the function 𝑧 = 𝑥2𝑦2.

𝑑𝑧 = 2x𝑦2𝑑𝑥 + 2𝑥2𝑦𝑑𝑦

𝑑𝑧 = 2x𝑦2𝑑𝑥 + 𝑥2𝑦𝑑𝑦

𝑑𝑧 = x𝑦2𝑑𝑥 + 2𝑥2𝑦𝑑𝑦

𝑑𝑧 = x𝑦2𝑑𝑥 + 𝑥2𝑦𝑑𝑦

63. 𝑧 = 𝑥 𝑦 funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = 𝑥 . Find total differential of the function = 𝑥 . 𝑦 𝑦

1 𝑥 𝑑𝑧 = 𝑦 𝑑𝑥 − 𝑦2 𝑑𝑦

1 𝑥 𝑑𝑧 = 𝑦 𝑑𝑥 + 𝑦2 𝑑𝑦

1 𝑥 𝑑𝑧 = − 𝑦 𝑑𝑥 − 𝑦2 𝑑𝑦

1 1 𝑑𝑧 = 𝑦 𝑑𝑥 − 𝑦2 𝑑𝑦

62. 𝑧 = ln(𝑥 + 𝑦) funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = ln(𝑥 + 𝑦). Find total differential of the function 𝑧 = ln(𝑥 + 𝑦).

𝑑𝑧 = 1 𝑥+𝑦 𝑑𝑥 + 1 𝑥+𝑦 𝑑𝑥 − 1 𝑥+𝑦 𝑑𝑦 𝑑𝑦

𝑑𝑧 = − 1 𝑥+𝑦 𝑑𝑥 + 2 𝑥+𝑦 𝑑𝑦

𝑑𝑧 = 2 𝑥+𝑦 𝑑𝑥 + 2 𝑥+𝑦 𝑑𝑦

61. 𝑧 = ln(𝑥𝑦) funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = ln(𝑥𝑦). Find total differential of the function 𝑧 = ln(𝑥𝑦).

𝑑𝑧 = 1 𝑑𝑥 + 𝑥 1 𝑑𝑦 𝑦

𝑑𝑧 =1 𝑑𝑥 − 𝑥 𝑑𝑧 = − 𝑥

𝑑𝑧 =2 𝑑𝑥 + 𝑥1 1 𝑑𝑦 𝑦 𝑑𝑥 +

𝑧 = sin(𝑥2 − 𝑦2) funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = sin(𝑥2 − 𝑦2). Find total differential of the function 𝑧 = sin(𝑥2 − 𝑦2).

𝑑𝑧 = 2 𝑥𝑐𝑜𝑠(𝑥2 − 𝑦2) 𝑑𝑥 − 2𝑦𝑐𝑜𝑠(𝑥2 − 𝑦2)𝑑𝑦

𝑑𝑧 = 2 𝑥𝑐𝑜𝑠(𝑥2 − 𝑦2) 𝑑𝑥 − 𝑦𝑐𝑜𝑠(𝑥2 − 𝑦2)𝑑𝑦

𝑑𝑧 = xcos(x2 − y2) dx − 2ycos(x2 − y2)dy

𝑑𝑧 = 𝑥𝑐𝑜𝑠(𝑥2 − 𝑦2) 𝑑𝑥 − 𝑦𝑐𝑜𝑠(𝑥2 − 𝑦2)𝑑𝑦

𝑧 = 𝑒𝑥2+𝑦2 funksiyaning to’liq differensialini toping. Найдите полный дифференциал функции 𝑧 = 𝑒𝑥2+𝑦2 . Find the total differential of the function 𝑧 = 𝑒𝑥2+𝑦2 .

𝑑𝑧 = 2𝑥𝑒𝑥2+𝑦2 𝑑𝑥 + 2𝑦𝑒𝑥2+𝑦2 𝑑𝑦

𝑑𝑧 = 2𝑥𝑒𝑥2+𝑦2 𝑑𝑥 − 2𝑦𝑒𝑥2+𝑦2 𝑑𝑦

𝑑𝑧 = 𝑥𝑒𝑥2+𝑦2 𝑑𝑥 + 2𝑦𝑒𝑥2+𝑦2 𝑑𝑦

𝑑𝑧 = 𝑥𝑒𝑥2+𝑦2 𝑑𝑥 + 𝑦𝑒𝑥2+𝑦2 𝑑𝑦

58. 𝑧 = 𝑥2 + 𝑦2 funksiyaning to’la differensialini toping. Найдите полный дифференциал функции 𝑧 = 𝑥2 + 𝑦2. Find total differential of function 𝑧 = 𝑥2 + 𝑦2.

𝑑𝑧 = 2𝑥𝑑𝑥 + 2𝑦𝑑𝑦

𝑑𝑧 = 𝑥𝑑𝑥 + 𝑦𝑑𝑦

𝑑𝑧 = 2𝑥𝑑𝑥 − 2𝑦𝑑𝑦

𝑑𝑧 = −𝑥𝑑𝑥 + 𝑦𝑑𝑦

𝑧 = 𝑥2 + 2𝑦2 sirtga (1,1,3) nuqtada o’tkazilgan urinma tekislik tenglamasini yozing. Напишите уравнение касательной плоскости поверхности 𝑧 = 𝑥2 + 2𝑦2 в точке (1,1,3). Write equation of a tangent plane of surface 𝑧 = 𝑥2 + 2𝑦2 at point (1,1,3).

2𝑥 + 4𝑦 − 𝑧 − 3 = 0

𝑥 + 4𝑦 − 𝑧 − 3 = 0

2𝑥 + 𝑦 − 𝑧 − 3 = 0

56. Normal tenglamasini ko’rsating. Укажите каноническое уравнение нормали. Find canonical equation of normal.

𝑥−𝑥0 = 𝑦−𝑦0 = 𝑧−𝑧0 𝑓′(𝑥0;𝑦0) 𝑓′(𝑥0;𝑦0) −1

𝑥+𝑥0 = 𝑦−𝑦0 = 𝑧−𝑧0 𝑓′(𝑥0;𝑦0) 𝑓′(𝑥0;𝑦0) −1

𝑥−𝑥0 = 𝑦+𝑦0 = 𝑧−𝑧0 𝑓′(𝑥0;𝑦0) 𝑓′(𝑥0;𝑦0) −1

𝑥+𝑥0 = 𝑦+𝑦0 = 𝑧−𝑧0 𝑓′(𝑥0;𝑦0) 𝑓′(𝑥0;𝑦0) −1

55. Urinma tekislik tenglamasini ko’rsating. Укажите уравнение касательной плоскости. Find formula of a tangent plane

𝑧 − 𝑧O = 𝑓′(𝑥 ; 𝑦) · (𝑥 − 𝑥) + 𝑓′(𝑥 ; 𝑦 ) · (𝑦 − 𝑦 )

𝑧 + 𝑧O = 𝑓′(𝑥 ; 𝑦 ) · (𝑥 − 𝑥 ) + 𝑓′(𝑥 ; 𝑦 ) · (𝑦 +𝑦 ) 𝑥 O O

𝑧 − 𝑧O = 𝑓′(𝑥 ; 𝑦 O) · (𝑥 + 𝑥 𝑥 O O) + 𝑓′(𝑥 ; 𝑦 · (𝑦 − 𝑦 )

𝑧 − 𝑧O = 𝑓′(𝑥 ; 𝑦 ) · (𝑥 + 𝑥 ) + 𝑓′(𝑥 ; 𝑦 ) · (𝑦 + 𝑦 )

54. 𝑓(𝑥, y) funksiyaning 𝑦 bo’yicha xususiy hosila formulasini toping. Найти формулу частной производной функции 𝑓(𝑥, y) по 𝑦. Find formula of partial derivative of the function 𝑓(𝑥, y) with respect to 𝑦.

𝑓′𝑦 = 𝑓′𝑦 = 𝑓′𝑦

lim∆𝑦→O = lim∆𝑦→O = lim∆𝑦→O

𝑓(𝑥;𝑦+∆𝑦)−𝑓(𝑥;𝑦) ∆𝑦 𝑓(𝑥;𝑦−∆𝑦)−𝑓(𝑥;𝑦) ∆𝑦 𝑓(𝑥;𝑦+∆𝑦)+𝑓(𝑥;𝑦)

∆𝑦 =𝑓′𝑦 = lim∆𝑦→O 𝑓(𝑥+∆𝑦)−𝑓(𝑥;𝑦) ∆𝑦

53. 𝑓(𝑥, y) funksiyaning 𝑥 bo’yicha xususiy hosila formulasini toping. Найти формулу частной производной функции 𝑓(𝑥, y) по 𝑥. Find formula of partial derivative of the function 𝑓(𝑥, y) with respect to 𝑥.

lim∆𝑥→O = lim∆𝑥→O

𝑓(𝑥+∆𝑥;𝑦)−𝑓(𝑥;𝑦) ∆𝑥 𝑓(𝑥+∆𝑥;𝑦)+𝑓(𝑥;𝑦) ∆𝑥 =𝑓′𝑥

=𝑓′𝑥 = lim∆𝑥→O = lim∆𝑥→O 𝑓(𝑥−∆𝑥;𝑦)−𝑓(𝑥;𝑦) ∆𝑥 𝑓(𝑥+;𝑦)−𝑓(𝑥;𝑦).

Ikki o’zgaruvchili 𝑓(𝑥, y) funksiyaning to’la ottirmasi formulasini toping. Найти формулу полного приращения функции двух переменных 𝑓(𝑥, y). Find formula of total increment of a function of two variables 𝑓(𝑥, y).

∆𝑓 = 𝑓(𝑥 + ∆𝑥; 𝑦 + ∆𝑦) − 𝑓(𝑥; 𝑦)

∆𝑓 = 𝑓(𝑥 + ∆𝑥 + ∆𝑦) − 𝑓(𝑥; 𝑦)

∆𝑓 = 𝑓(𝑥 + ∆𝑥; 𝑦 + ∆𝑥) − 𝑓(𝑥; 𝑦)

70. 𝑧 = 𝑥3 + 𝑦2 funksiya berilgan 𝛛2𝑧 ni toping. Найдите 𝛛2𝑧 функции 𝑧 = 𝑥3 + 𝑦2. Find 𝛛2𝑧 𝛛𝑦2

𝛛2𝑧 = 2 𝛛𝑦2 of function 𝑧 = 𝑥3 + 𝑦2. 𝛛𝑦2 𝛛𝑦2

𝑧 = ln(𝑥2 + 𝑦2) funksiya berilgan, 𝛛𝑧 𝛛𝑦 ni toping. Найдите 𝛛𝑧 𝛛𝑦 функции 𝑧 = ln(𝑥2 + 𝑦2). Find 𝛛𝑧 𝛛𝑦 of the function = ln(𝑥2 + 𝑦2) .

𝛛𝑧 = 2𝑦 𝛛𝑦 𝑥2+𝑦2

𝛛𝑧 = 4𝑦 𝛛𝑦 𝑥2+𝑦2

𝛛𝑧 = − 2𝑦 𝛛𝑦 𝑥2−𝑦2

𝛛𝑧 = 𝑦 𝛛𝑦 𝑥2+𝑦2

математика 2

Quiz

•

Other

•

1st Grade

•

Practice Problem

•

Hard

Mira Seidakbar

FREE Resource

Student preview

50 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Ikki o’zgaruvchili 𝑓(𝑥, y) funksiyaning 𝑦 ga nisbatan xususiy orttirma formulasini toping. Найти формулу частного приращения функции двух переменных 𝑓(𝑥, y) по
y. Find formula of partial increment of a function of two variables 𝑓(𝑥, y) with respect to
𝑦.

∆𝑦𝑓 = 𝑓(𝑥; 𝑦 + ∆𝑦) − 𝑓(𝑥; 𝑦)

∆𝑦𝑓 = 𝑓(𝑥 + ∆𝑦) − 𝑓(𝑥; 𝑦)

∆𝑦𝑓 = 𝑓(𝑥; 𝑦 + ∆𝑦) − 𝑓(𝑥; ∆𝑦)

∆𝑦𝑓 = 𝑓(𝑥 + 𝑦) − 𝑓(𝑥; 𝑦)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Ikki karrali integralning xossasi to’g’ri berilgan javobni toping. Найти правильное свойство двойного интеграла. Find the correct property of triple integral.

∬𝐷 (𝑓1(𝑥; 𝑦) − 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 − ∬𝐷

𝑓2(𝑥; 𝑦)𝑑𝑥𝑑𝑦

∬𝐷 (𝑓1(𝑥; 𝑦) − 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = 3 ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 − ∬𝐷

𝑓2(𝑥; 𝑦)𝑑𝑥𝑑𝑦

∬𝐷 (𝑓1(𝑥; 𝑦) − 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 − 3 ∬𝐷

𝑓2(𝑥; 𝑦)𝑑𝑥𝑑𝑦

∬𝐷 (𝑓1(𝑥; 𝑦) − 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 + ∬𝐷

𝑓2(𝑥; 𝑦)𝑑

𝑥𝑑𝑦.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Ikki karrali integralning xossasi to’g’ri berilgan javobni toping. Найти правильное свойство двойного интеграла Find the correct property of triple integral.

∬𝐷 (𝑓1(𝑥; 𝑦) + 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 + ∬𝐷

𝑓2(𝑥; 𝑦)𝑑𝑥𝑑𝑦

∬𝐷 (𝑓1(𝑥; 𝑦) + 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 + 𝑘 ∬𝐷

𝑓2(𝑥; 𝑦)𝑑𝑥𝑑𝑦

∬𝐷 (𝑓1(𝑥; 𝑦) + 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = 3 ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 + ∬𝐷

𝑓2(𝑥; 𝑦)𝑑𝑥𝑑𝑦

∬𝐷 (𝑓1(𝑥; 𝑦) + 𝑓2(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = −𝑘 ∬𝐷

𝑓1(𝑥; 𝑦)𝑑𝑥𝑑𝑦 + ∬𝐷

𝑓2(𝑥; 𝑦)𝑑𝑥𝑑𝑦

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

99. Ikki karalla integralning xossasi to’g’ri berilgan qatorni toping. Найти правильное свойство двойного интеграла. Find the correct property of double integral

∬𝐷

𝑐 · 𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦 = 𝑐 · ∬𝐷

𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦, 𝑐 − 𝑐𝑜𝑛𝑠𝑡

∬ 𝑐 · 𝑓(𝑥; 𝑦)𝑑𝑦𝑑𝑥 = 1 · ∬ 𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦, 𝑐 − 𝑐𝑜𝑛𝑠𝑡

𝐷 c 𝐷

∬𝐷 𝑐 · 𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦 = ∬𝐷 𝑓(𝑥; 𝑦)𝑑𝑦𝑑𝑥, 𝑐 − 𝑐𝑜𝑛𝑠𝑡

∬𝐷

𝑐 · 𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦 = 3𝑐 · ∬𝐷

𝑓(𝑦; 𝑥)𝑑𝑥𝑑𝑦, 𝑐 − 𝑐𝑜𝑛𝑠𝑡

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

А(1,0) nuqtadan В(0,2) nuqtagacha oraliqda ∫ (𝑥𝑦 − 1)𝑑𝑥 + 𝑥2𝑦𝑑𝑦

egri chiziqli

integralni hisoblang. Вычислить криволинейный интеграл ∫ (𝑥𝑦 − 1)𝑑𝑥 + 𝑥2𝑦𝑑𝑦 от

точки А(1,0) до точки В(0,2). Calculate curvilinear integral ∫ (𝑥𝑦 − 1)𝑑𝑥 + 𝑥2𝑦𝑑𝑦
from point А(1,0) to point В(0,2).

-1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

𝑥 = 𝑐𝑜𝑠3𝑡, 𝑦 = 𝑠𝑖𝑛3𝑡 astroid yoyi bo’yicha 𝐸(−1, 0) va 𝐻(0,1) nuqtalar orasida

∫ (43√𝑥 − 3√𝑦)𝑑𝑆

egri chiziqli integralni hisoblang. Вычислить криволинейный

интеграл ∫ (43√𝑥 − 3√𝑦)𝑑𝑆

от точки 𝐸(−1, 0) до точки 𝐻(0,1) по дуге астроиды

𝑥 = 𝑐𝑜𝑠3𝑡, 𝑦 = 𝑠𝑖𝑛3𝑡. Calculate line integral ∫ (43√𝑥 − 3√𝑦)𝑑𝑆

from point

𝐸(−1, 0) to point 𝐻(0,1) a long the arc of the astroid 𝑥 = 𝑐𝑜𝑠3𝑡, 𝑦

𝑠𝑖𝑛3𝑡.

− 46

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

96. ∫ 𝑑𝑆

egri chiziqli integralni hisoblang, bunda 1 to’g’ri chiziqning

𝛾 𝑥−𝑦 2
A(0,2) va B(4,0) nuqtalar orasiga qismi. Вычислить криволинейный интеграл ∫ 𝑑𝑆 ,
𝛾 𝑥−𝑦
где γ – отрезок прямой 𝑦 = 1 𝑥 − 2, заключенного между точками 𝐴(0, 2) и 𝐵(4, 0).
2
Calculate the curvilinear integral ∫ 𝑑𝑆 , where γ is a straight line segment 1 ,
𝛾 𝑥−𝑦 2
enclosed between points A(0,2) and B(4,0)

𝑙𝑛2

√5𝑙𝑛2

√5

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математика 2

50 questions

Ikki karrali integralning xossasi to’g’ri berilgan javobni toping. Найти правильное свойство двойного интеграла. Find the correct property of triple integral.

Ikki karrali integralning xossasi to’g’ri berilgan javobni toping. Найти правильное свойство двойного интеграла Find the correct property of triple integral.

99. Ikki karalla integralning xossasi to’g’ri berilgan qatorni toping. Найти правильное свойство двойного интеграла. Find the correct property of double integral

Ikki karrali integraldan foydalanib, ellips bilan chegralangan sohani toping. C помощью двойного интеграла найти площадь, ограниченную эллипсом. Using a double integral, find the area enclosed by an ellipse.

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