What is the formula of curvature

What is the formula of curvature

The absolute value of the second derivative divided by 1 plus the derivative squared to the power of 1.5

The problem of curvature formula in high number books
In other words, it is written in the book of higher numbers that we derive the formula of curvature according to k = | DA / DS |
Let the Cartesian coordinate equation of the curve be y = f (x), and f (x) have the second derivative (when f '(x) is continuous) because Tan a = y', so sec ^ 2 A * (DA / DX) = y ''
Er, how did Tan a = y 'come from? And shouldn't the derivation of Tan a be equal to SEC ^ 2 a? How did DA / DX come from

Tana is the slope, the slope is the derivative of y to x, dy / DX = k = Tana
D (Tan a) = (SEC a) ^ 2 Da, is the formula in the book
y'=tan a
dy'/dx=d(tan a)/dx
y''=sec^(2)a da/dx
What's the problem?

How did you get the curvature formula?
 

This is the curvature formula under the rectangular coordinate equation
 
The derivation process is as follows:
 

Finding the second derivative of ellipse 4x ^ 2 + y ^ 2 = 4

4X ^ 2 + y ^ 2 = 4 to get x ^ 2 + y ^ 2 / 4 = 1. Obviously, y '= - 4x / Y and y' '= [(- 4 * y) - (- 4x * y')] / Y & # 178; y '' = 4 (XY '- y) / Y & # 178; if you want to get an expression without y', you can get y '' = 4 [x (- 4x / y) - y] / Y & # 178; y '' = 4 (- 4x & # 178;) / (Y & # 178;)

Find the curvature of ellipse 4x & # 178; + Y & # 178; = 4 at point (0,2)

2

What are the characteristics of normal distribution curve and what is the standard normal distribution curve?
If you take the course of Biostatistics, you have to take the final exam
The children's shoes on the first floor are too abstract.
I'm at school now, far away from home. It's not realistic to go back to read!

Senior three mathematics teacher's edition has detailed, probably the image is an opening downward parabola
I'm not saying that the mathematics book of senior three published by PEP has detailed contents. There's no way to make clear one or two sentences here, right
This is a book. You can ask me if you don't understand

The coordinates of the vertex of normal distribution curve
Know whether the standard deviation of the mean can calculate the vertex coordinates of the curve

The probability density function expression of normal distribution shows that
p(x)=1/[√(2π)σ]e^{-(x-u)²/(2σ²)}
It can be seen that the curve is symmetric with respect to x = u, and the maximum value on the axis of symmetry is 1 / [√ (2 π) σ]
Where u is the mean value, that is, the mathematical expectation, and σ is the standard deviation
Therefore, the vertex coordinates of the curve are (U, 1 / [√ (2 π) σ])

What is the difference between normal distribution curve and t curve?

Like normal distribution, t distribution is a bell shaped distribution with single peak symmetry. Its axis of symmetry passes through the average of distribution, and the transverse axis of t distribution curve is its asymptote in both positive and negative directions
Compared with normal distribution, t-distribution curve is low and sharp in the middle, and high and gentle at both ends. The biggest characteristic of t-distribution is that it is essentially a family of distributions. The shape of each t-distribution is restricted by an index called degree of freedom. There is a t-distribution corresponding to one degree of freedom. With the increase of degree of freedom, the middle of t-distribution curve is higher and higher, but the two ends are lower and lower, When the degree of freedom approaches infinity, t distribution becomes normal distribution

How to make standard normal distribution probability density function curve with Excel

Because it is the standard positive distribution, i.e. μ = 0, σ = 1, the following steps are used to draw the curve:
1. Input formula in A1 = (row (A1) - 1) * 0.25-3
2. Input formula = NORMDIST (a1,0,1,0) in B1
3. Drop down to copy the above two formulas to a25 and B25 respectively
4. Take column a as the x-axis and column B as the y-axis to insert "XY scatter diagram", and select "scatter diagram with smooth line" as the type of scatter diagram
OK, give me a good comment!

How to draw normal distribution curve

It needs to be done with Excel software, specifically: > > t = 0:1:1000; y = normpdf (x, 0,1); u = int (y, 0, t); plot (T, y) undefined function or variable 'x' > > t = 0:1:1000; y = normpdf (x, 0,1); u = int (y, 0, t); plot (T, y) undefined function or VA