Find an expression for y given 𝒅𝒚 ÷ 𝒅𝒙= 𝟕𝒙^𝟓

Find an expression for y given 𝒅𝒚 ÷ 𝒅𝒙 = 𝒙^_¾

dy = ∫ −𝟏𝟐𝐱^−𝟒 dx solve it;

Given f ‘(x) = ∫ ( 𝟐 ÷ 𝒙 + 𝟑 ÷ 𝒙^𝟐 + 𝟏 ÷ 𝒙^𝟓 ) dx

Integrate ∫ 𝟑 ÷ 𝒙½ dx

Find y as a function of x if 𝒅𝟐𝒚 ÷ 𝒅𝒙𝟐 = 2x when x = 2, y = 7 

Integrate ∫ (𝒘 + 𝟏÷𝒘 ) (𝒘 − 𝟏÷𝒘 ) dx

Calculate ∫ 𝒙^𝟕 𝒅𝒙

If ∫ 𝒇(𝒙)𝒅𝒙 = 𝒙𝒆^{− 𝐥𝐨𝐠|𝒙|} + f(x), then f(x) is

If f (t) =∫𝐭−𝐭  𝐝𝐱 ÷ 𝟏+𝐱𝟐 , then f’ 

The existence of first order partial derivatives implies continuity 

The gradient of a function is parallel to the velocity vector of the level curve

y = (8 + 𝒙³ ) (𝒙³ - 8)

If (x, y, z, t) = xy + zt + x2y z t; x = k3; y = k2; z = k; t = √𝒌

Find 𝒅𝒇÷𝒅𝒕 at k = 1

If (x, y) = x2 + y3; x = t2 + t3 ; y = t3 + t9 find 𝒅𝒇÷𝒅𝒕 at t=1.

Necessary condition of Euler’s theorem is

If f(x, y) = 𝒙+𝒚÷𝒚 , x 𝒅𝒙÷𝒅𝒛 + y 𝒅𝒛÷𝒅𝒚=? 

Find the approximate value of [𝟎. 𝟗𝟖𝟐 + 𝟐. 𝟎𝟏𝟐 + 𝟏. 𝟗𝟒𝟐]½

f (x,y) = 𝒙𝟑+𝒚3 ÷ 𝒙𝟗𝟗+𝒚𝟗𝟖𝒙+𝒚𝟗𝟗 find the value of fy at (x, y) = (0, 1)

f (x, y) = x3 + xy2 + 901 satisfies the Eulers theorem

  𝒍𝒊𝒎
𝒏 → ∞ [ 𝒏÷𝟏+𝒏^𝟐 + 𝒏÷𝟒+𝒏^𝟐 + 𝒏÷𝟗+𝒏^𝟐 + …. + 𝟏÷𝟐𝒏 ] is equal to

Question 29 For homogenous function with no saddle points we must have the minimum value as

The derivates of f(x) = ∫𝒙³𝒙² 𝟏÷𝒍𝒐𝒈𝒕 dt, (x>0) is  

∫𝒃−𝒄𝟎 𝒇 𝒏  (x + a) dx =

∫𝒙𝟎 𝒙𝟑𝒅𝒙 ÷ (𝒙𝟐+𝟒)² =

The points of intersection of F1(x) =∫x2 (𝟐𝐭 − 𝟓)𝐝𝐭 𝐚𝐧𝐝 𝐟𝟐(x) =∫x0𝟐𝐭 𝐝𝐭, 𝐚𝐫𝐞

The rate of increase of bacteria in a certain culture is proportional to the number present. If it double 5 hours then in 25 hours its number would be

The degree of the 3𝒅^𝟐𝒚÷𝒅𝒙^𝟐 = {𝟏 + ( 𝒅𝒚÷𝒅𝒙)^𝟐 }^𝟑/𝟐 is differential equation 

The differential equation representing the family of curves y2 = 2c(x+√𝒄), where c is a positive perimeter, is of

The order and degree of the differentiate equations (𝟏 + 𝟑 𝒅𝒚÷𝒅𝒙)𝟐/𝟑 – 4 ( 𝒅𝟑𝒚÷𝒅𝒙𝟑 ) are

The solution of the differential equation y - x 𝒅𝒚÷𝒅𝒙 = a(𝒚𝟐 + 𝒅𝒚÷𝒅𝒙) is 

Compute the sum of 4 digit numbers which can be formed with four-digit 1, 3, 5, 7 if each digit is used once in each engagement: