Try to find the analytic function f (z) = u + IV with v = Y / x ^ 2 + y ^ 2 as imaginary part, and satisfy f (2) = 0

Try to find the analytic function f (z) = u + IV with v = Y / x ^ 2 + y ^ 2 as imaginary part, and satisfy f (2) = 0

The process is shown in the picture. If you don't understand, you can ask me again

Given that the derivative of Y is y ', y = 3x + 2XY' (5), then y '(5) =? Y' (2) =?

Let a = y '(5)
Then y = 3x ^ 2 + 2xa
y'=6x+2a
So y '(5) = 30 + 2A = a, a = - 30
That is, y = 3x ^ 2-60x
y'=6x-60
y'(2)=-48

Let z = x + iy and the imaginary part of the analytic function f (z) be v = y3-3x2y, then the real part U of F (z) can be taken as ()
A.x2-3xy2 B.3xy2-x3
C.3x2y-y3 D.3y3-3x3

From Cauchy Riemann condition V '(x) = - U' (y), V '(y) = u' (x), u '(y) = - 6xy, u' (x) = 3Y & sup2; - 3x & sup2;
So choose B

XY sin (π y ^ 2) = 0 determines that y is a function of X

In fact, there is a differential D π y ^ 2 first
Here π y ^ 2 is regarded as a function f (y) with y as a variable
D π y ^ 2 / DX
(the premise here is that the derivative can be regarded as the quotient of the differential.)
The denominator numerator multiplied by Dy becomes
(dπy^2/dy)*(dy/dx)
Then the term on the left can be regarded as the derivative of F (y), i.e. 2 π y
On the right is the derivative of Y with respect to x, y '
So the derivative of π y ^ 2 becomes 2 π y * y

What's the title of the application problem after unit 2 "the addition and subtraction within ten thousand"

What's in the bookstore

If f (x) satisfies 2F (x) + 3f (- x) = x2 + X, then f (x)=______ ．

∵ 2F (x) + 3f (- x) = x2 + X, ① ∵ 2F (- x) + 3f (x) = x2-x, ② × 3 − ① × 25: F (x) = X25 − x, so the answer is X25 − X

If the solutions of the binary linear equations ax + y = 2, x-by = 2 and 2x + 3Y = 4, 2x-5y = - 12 about X, y are the same, find the values of real numbers a and B

Solving equations
2x+3y=4
2x-5y=-12
have to
x=-1
y=2
Substituting x = - 1, y = 2
Ax + y = 2, x-by = 2
-a+2=2
-1-2b=2
∴a=0
b=-3/2

From 0, 1, 2 The absolute value of the difference between one digit number and one hundred digit number is 8______ One

According to the meaning of the question, there are two situations in which the absolute value of the difference between 0 and 9 is equal to 8: 0 and 8, 1 and 9. There are two situations to discuss: ① when the number of individual and hundred is 0 and 8, there is a82a22; ② when the number of individual and hundred is 1 and 9, there is a71a71a22. A total of a82a22 + a71a71a22 = 210, so the answer is 210

It is known that the distance from the intersection of the image of positive scale function and hyperbola to the abscissa axis is 1, and the distance to the ordinate axis is 2

From the meaning of the problem, we know that the image and hyperbola of positive proportion function pass through points (2, 1), (2, - 1) (- 2, 1) (- 2, - 1). So we can get their function expression as follows: y = 12x, y = 2x; y = - 12x, y = - 2x

For the concepts of positive and negative numbers, why can't we simply understand that the number with a positive sign is positive and the number with a sign is negative?

Because there is a special number 0
+0 is not a positive number
-0 is not a negative number
So it can't be understood that way