Mr. Hermes Rozsa Iglesias

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These are questions asked by herclau


Hi MaplePrimes,

I want to find the arithmetic mean of all radius from ellipse sector.

Let me explain: I want the average radius of the interval in red
on the ellipse that is between the two radios


Is it possible to reproduce this MathCad example in Maple?

The quantity diff(y)./diff(x) is an approximate derivative.

  • x = [1 2 3 4 5];
    y = diff(x)
    y =
         1     1     1     1
    z = diff(x,2)
    z =
         0     0     0


  • A = rand(1,3,2,4);

diff(A) is the first-order difference along dimension 2.

diff(A,3,4) is the third-order difference along dimension 4.

The function diff of Matlab calculates differences between adjacent elements of X along the first array dimension whose size does not equal 1

Is there a similar function in Mape?

I try to reproduce in Maple this document in pdf. In it you can see the code in MathCad to find the roots of a system of equations by the method of Draghilev.
After seeing some of the codes posted in the Maple forum where the development of the method is shown and reading the document in the Application Center, some questions arise.
When the deferential ecacuion system is divided, in this case stored in variale b [i], by b [i] / (b [1] ^ 2 + b [2] ^ 2) ^ 0.5; i = 1..n + 1
Why, as I could see in some systems, the first two differential equations are taken and in others it takes three?
And in what systems does it divide at all?



In this case in my transfer of code from Mathcad to Maple I do not get the initial values of the system fsolve calculates indefinitely



How to find the points indicated in the graph of the following function:
(1.25 * y-sqrt (abs (x))) ^ 2 + x ^ 2-1,

I have used the Taks: the Second Derivative Test. Without results, as I show below:




Critical Points and the Second Derivative Test

Objective Function f




smartplot[x, y]((1.25*y-sqrt(abs(x)))^2+x^2-1 = 0)




List of Independent Variables

v := [x, y]

[x, y]


Equations Nabla(f) = 0

convert(Student[MultivariateCalculus][Gradient]((1.25*y-abs(x)^(1/2))^2+x^2-1, [x, y]), list)

[-(1.25*y-abs(x)^(1/2))*abs(1, x)/abs(x)^(1/2)+2*x, 3.1250*y-2.50*abs(x)^(1/2)]


Critical Points

temp := remove(has, solve([-(1.25*y-abs(x)^(1/2))*abs(1, x)/abs(x)^(1/2)+2*x, 3.1250*y-2.50*abs(x)^(1/2)], v, Explicit), I); convert({seq(eval(v, temp[k]), k = 1 .. nops(temp))}, list)



Second Derivative Test

Student[MultivariateCalculus][SecondDerivativeTest]((1.25*y-abs(x)^(1/2))^2+x^2-1, v = [])

LocalMin = [], LocalMax = [], Saddle = []


Hessians and their Eigenvalues

Temp := [Student[MultivariateCalculus][SecondDerivativeTest]((1.25*y-abs(x)^(1/2))^2+x^2-1, v = [], output = hessian)]; for k to nops(Temp) do Temp[k], convert(LinearAlgebra[Eigenvalues](Temp[k]), list) end do

Error, (in LinearAlgebra:-Eigenvalues) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values





Download Heart_Critical_Points_and_the_Second_Derivative_Test.mw




How to solve with maple using integration by parts the integral?int(sec(x)^(n),x);
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