Please explain the geometric meaning of gradient

Please explain the geometric meaning of gradient

Taking the binary function f (x, y) as an example, first of all, the gradient of F (x, y) at a certain point (x0, Y0) is a vector, and its direction is the direction where the function value of F (x, y) changes the fastest at that point, that is, the direction where the directional derivative is the largest, and its modulus is equal to the maximum value of the directional derivative at that point

Geometric significance of gradient divergence curl

Gradient is the direction vector with the largest change rate of function
If the divergence is greater than 0, the outflow is greater than the inflow, indicating that there is a source in the closed surface,

What is the gradient of a function?

The gradient of a scalar field is a vector field. The gradient at a certain point in the scalar field points to the fastest growing direction of the scalar field, and the length of the gradient is the maximum rate of change. More strictly speaking, the gradient of a function from the Euclidean space RN to R is the best linear approximation at a certain point in RN

If x-3y = 3, then 7 + 6y-2x=

1

Given that the point is on the hyperbola x216 − Y29 = 1, and the distance from the right collimator of the hyperbola is exactly the mean of the distance between the two focal points of the hyperbola, then the abscissa of P is______ ．

If P is in the right branch of hyperbola, then | Pf1 | = | PF2 | + 2A = ed + 2A

In the triangle ABC, ab = 5, BC = 6, ad = 4 on the side of BC, find the length of AC

If AC = 5, ad is the middle line, BD = 3345 Pythagorean theorem, so ad is perpendicular to BC, AC = AB = 5

Given (2x-1) + I = y - (3-y) I, where x is a pure imaginary number and Y is a real number, find the value of X and y
RT

Let x = AI, where a is a real number
2ai-1+i=y-(3-y)i
(2a+1)i-1=(y-3)i+y
2a+1=y-3
-1=y
y=-1
a=-5/2
x=-5i/2

Given the function f (x) = 2Sin (2x + \ 3), find
For the given function f (x) = 2Sin (2x + π / 3), find 1. Find the minimum positive period of the function (3). Find the monotone decreasing interval of F (x)

T=2π/w=2π/2=π
2）2kπ+π/2

It is known that the hypotenuse ab of RT △ ABC is 5cm, the right angle AC is 4cm and BC is 3cm. The surface area of the geometry is ()
A. 22.56πcm2B. 16.8πcm2C. 9.6πcm2D. 7.2πcm2

A geometry composed of two cones is obtained by rotating a circle around a straight line ab. the height of the hypotenuse of the right triangle is CD = 3 × 45 = 125cm, then the circumference of the circle with radius 125 = 245 π cm, and the surface area of the geometry is 12 π × 245 × (4 + 3) = 845 π = 16.8 π cm2, so B

1. The Φ of power factor cos Φ refers to? 2. The active power of symmetrical three-phase circuit P = root 3 * the φ in uicos Φ refers to?
A. Impedance angle
B. Angle between phase voltage and phase current
C. The angle between line current and line voltage
D. Others__________________

Answer: B. the angle between phase voltage and phase current