## MaplePrimes Questions

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## Problems saving a worksheet as task...

Hi,

I recently moved from Windows 10 to Windows 11. I am using Maple 2022.2, and I got that installed and working OK.

I have four Maple worksheets that I have saved as tasks on Windows 10, but my OS move requires some adjustments. When I try save the modified worksheets to the default Maple help database, I get an error saying that the database is read-only. When I try to make a new database file, Maple asks if it should create it, but then I get an error that Maple can't open the new database.

Suggestions?

Thanks,

Jno.

## How to find the following:...

How do I do the following:
Im having trouble plotting them on maple 2024 as well

For each function ( f(x) ) given below, define ( F(x) = \integral ,from a to x ,  f(t) \, dt \).

Is $$F(x)$$ an antiderivative of $$f(x)$$? Plot $$f(x)$$ and $$F(x)$$ in the same window for $$x \in [a, b]$$. How is $$F(x)$$ related to the area between $$f(x)$$ and the x-axis on $$[a, b]$$?

(a) ( f(x) = (1/x^2),  a = 1, , b = 10 )

(b) ( f(x) = sin x,  a = 0, , b = pi )

(c) ( f(x) = (1/4) x^4 - 2 x^3+ 4 x^2, , a = 0, , b = 5 )

(d) ( f(x) = (1/4) x^4 - 2 x^3 + 4 x^2, , a = 0, , b = 6 )

.

## Why is it that the two results of the higher order...

I reduced the order of two nonlinear equations and solved them numerically in this way. Why are the two results obtained the same?
directdsolve919.mw

## Plot approximations ...

I have the function  and derivate with respect to ν and make the change variable ν=1/t it seems it doesn’t work. I put the derivate of 1/t => -1/t2 by hand  (could it be done by “dchange” the hole transformation ?)

I want to approximate the value of the integral. It seems that the solution of the equation and plot in 2 situations for low-frequency ν < 1014  and for high frequency so  when the exponential is dominated.

Thus plot the whole function E2 in the two situations. Could it be done with a series?

For value h := 6.62607015*10^(-34); c := 299792458; T := 273 + 24; k := 1.380649*10^(-23);

ec := 1.602176634*10^(-19); ν1 :=1012 ; ν2 := 1017 ;Tq := 1.765358264*10^(-19);

Could it be merged E2 into one plot for ν = 1012 .. 1017

PPh1.mw

## Cannot calculate the curve length of the complicat...

Hi everyone, I wrote a complex 3D curve expression and wanted to calculate its length (0..Pi), but Maple was always calculating and could not get the answer. The code and worksheet are attached.
The idea came from: https://www.mapleprimes.com/questions/239065-Curve-Length-2d-3d

 >
 >
 >
 (1)
 >
 >
 (2)

## Hints for Run Time...

Hi

How we can reduce run time for Cases III and IV ? (Maple 2016)

Thanks alot

Formula_II.mw

## Curve Length 2d 3d...

Good morning, I am trying to graph the length of the curve but Maple gives me an error. Please if someone can tell me how I can graph the curve in 2d and 3d.

plot([t*sin(t), t*cos(t), (2*sqrt(2))/3*t^(3/2),t, t = 0 .. Pi]) -> error

## As a small exercise line y wanted...

Just one more small geometry task to get to know Maple a little better:
In the 1st quadrant, point A is on the y-axis and points B, D, C are at a positively increasing distance from the origin on the x-axis. Let BD = DC = s/2 and angle ADB = 45°. Point D is therefore the center of BC. The area of ​​triangle ABC is 60, line AD = x and the length of AC = 19. We are looking for the length of line AB = y.

## Roots wanted ;-)...

A student wakes up at the end of the lecture and just catches the professor saying:
"... and the roots form an arithmetic sequence."

On the board there is a 5th degree polynomial as homework, but unfortunately the student only manages to write down
x^5 - 5x^4 - 35x^3 +
before the professor wipes the board.

But the student still finds all the roots of the polynomial.

And the roots now have to be calculated.

## How can I make the list into environment \begin{en...

I have a list

mylist := [[sqrt(-5*x^2 - 5*x - 1) = -4*x - 1, {-1/3, -2/7}], [sqrt(-5*x^2 - 5*x - 1) = x + 1, {-1/2, -2/3}], [sqrt(-5*x^2 - 5*x - 1) = 4*x + 3, {-2/3, -5/7}], [sqrt(-5*x^2 - 5*x + 4) = -5*x + 3, {1/2, 1/3}], [sqrt(-5*x^2 - 4*x + 2) = -5*x + 2, {1/3, 1/5}], [sqrt(-5*x^2 - 4*x + 2) = -2*x + 1, {-1/3, 1/3}]]

I tried
latex(mylist) and get

\left[\left[\sqrt{-5 x^{2}-5 x -1} = -4 x -1, \left\{-{\frac{2}{7}}, -
{\frac{1}{3}}\right\}\right], \left[\sqrt{-5 x^{2}-5 x -1} = x +1,
\left\{-{\frac{2}{3}}, -{\frac{1}{2}}\right\}\right], \left[
\sqrt{-5 x^{2}-5 x -1} = 4 x +3, \left\{-{\frac{5}{7}}, -{\frac{2}{3}}
\right\}\right], \left[\sqrt{-5 x^{2}-5 x +4} = -5 x +3, \left\{{\frac
{1}{2}}, {\frac{1}{3}}\right\}\right], \left[\sqrt{-5 x^{2}-4 x +2} =
-5 x +2, \left\{{\frac{1}{3}}, {\frac{1}{5}}\right\}\right], \left[
\sqrt{-5 x^{2}-4 x +2} = -2 x +1, \left\{-{\frac{1}{3}}, {\frac{1}{3}}
\right\}\right]\right]



How can I get  a latex like this?

\documentclass[12pt,a4paper]{article}
\usepackage[left=1.5cm, right=1.5cm, top=2cm, bottom=2cm]{geometry}
\usepackage{fouriernc}
\usepackage{enumitem}
\usepackage{amsmath}
\begin{document}
Solve the following equations:
\begin{enumerate}[label=\arabic*)]
\item $\sqrt{-5 x^{2}-5 x -1} = -4 x -1.$ \hfill Answer: $\left\{-{\dfrac{2}{7}}, -{\dfrac{1}{3}}\right\}.$
\item $\sqrt{-5 x^{2}-5 x -1} = x +1.$ \hfill Answer: $\left\{-{\dfrac{2}{3}}, -{\dfrac{1}{2}}\right\}.$
\item $\sqrt{-5 x^{2}-5 x -1} = 4 x +3.$ \hfill Answer: $\left\{-{\dfrac{5}{7}}, -{\dfrac{2}{3}}\right\}.$
\item $\sqrt{-5 x^{2}-5 x +4} = -5 x +3.$ \hfill Answer: $\left\{{\dfrac{1}{2}}, {\dfrac{1}{3}}\right\}.$
\item $\sqrt{-5 x^{2}-4 x +2} = -5 x +2.$ \hfill Answer: $\left\{{\dfrac{1}{3}}, {\dfrac{1}{5}}\right\}.$
\end{document}

## Loop not executing all value just taking 1st value...

Loop is not executing all values just considerinng 1st value of tau0 =0.3.

Also how to plot a 2D graph from the loop result

Attaching sheet with questions in the sheet:
for_loop_question_rec.mw

## transformation of PDE to ODE with special equation...

i already did  a lot of function transform but this one give me some error can anyone determine what is mistake of this equation?

pde_to_ode.mw

## Fixing a corrupt maple file (Maple 2022)...

I have some lecture notes and examples that suddenly appears to be corrupted. I am getting the following error code when trying to open the file: "There was a problem in the loading process, you worksheet may be incomplete."

I've tried the following trouvleshooting:

- Close and reopen Maple

- Restarting computer

- Tried different computer

note: I have no backup files as I do not have autosave switched on.

I have also tried looking into the solution posted on a previous question on this site (https://www.mapleprimes.com/questions/235363-How-To-Fix-Corrupted-Maple-File), i.e.  changing the file format to.xml and making changes but with no luck :(

Is anyone able to help me fix it and un-corrupt this file:

Lecture_2_-_notes.mw

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