How can I simplify the expression by applying equivalent infinitesimal  in symbolic computation?

For example,for small x,  limit(x/sin(x) + x, x = 0),  I want to get 1+x, rather than 1. In fact, how can I set an assumption that x is small and let the expression be simplified or replaced by other equivalent infinitesimal terms?

sol := {c[1, 1] = 18.00000000, c[1, 2] = -0., u[1, 1] = -.9000000000, u[1, 2] = 0., x[1, 1] = 3.600000000, x[1, 2] = -0.}
How we can assign each in solution1 individually as a Variable.

Dear all

I know how can I use gauss seidel to solve a linear system.

But, how can we add chebychev acceleration.

Thank you 

How do you find the fermat point of a triangle? (a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible.)

Hello, i'm new in maple and i don't know how to programming in it. i need to write two For loop in maple to make a matrix. i can write it simply in Matlab as:

Is it possible to open or import, and execute Maple Flow documents in Maple 2021?

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convODEPlot.mwODEPlot.mwert/ODEPlot.mw .

restart;
with(plots);
g := 32.2;
k := 0.1;
theta := Pi/5;
v := 50;

ode0 := diff(x(t), t $ 2) = 0, diff(y(t), t $ 2) = -g    

                                  
ode1 := diff(x(t), t $ 2) = -k*diff(x(t), t) - x(t) - 1/6*x(t)^3 + 1/120*x(t)^5, diff(y(t), t $ 2) = -g - k*diff(y(t), t) - y(t) - 1/6*y(t)^3 + 1/120*y(t)^5

ics := x(0) = 0, y(0) = 0, D(x)(0) = v*cos(theta), D(y)(0) = v*sin(theta)

dsolve([ode1, ics], numeric)

dsolve([ode0, ics])

display(plot([rhs(dsolve([ode0, ics])[1]), rhs(dsolve([ode0, ics])[2]), t = 0 .. 2], color = red), plot([rhs(dsolve([ode1, ics, numeric])[1]), rhs(dsolve([ode1, ics, numeric])[2]), t = 0 .. 2]), view = [0 .. 75, 0 .. 15])

Hi! Do you know maybe how to get this plot of ode1? I guess that computations are ok but I cannot get this plot.

with(VectorCalculus):

SetCoordinates(cartesian[x,y,z]):

TangentLine(z = f(r, theta), r = a, theta = b, coords = cylindrical[r, theta, z]) . le resultat de maple est une équation en x et y comment expliquer ce resulta s'il vous plait et merçi beaucoup.

Hello there,
I'd like to know, if there's any way of testing these following relations on Maple.
I've tried to look at the assume command, but without succes.

I'll link the tasks below as an example:

Text translation:
f(x) is given as cos(x). Show that |f(x)-P(x₀)| ≤ |x-x₀|, when x is a real number

Please help me solve the following problem with Maple commands:
Determine the equation of the line d, knowing that d passes through the point A(1,-2,3) and intersects both lines d1:(x-1)/2=y/1=(z+3)/ -2 and d2:(x-1)/-1=y/1=(z-3)/2. Thank you very much!

Any idea why I can't write Excel output to my standard Documents directory?

Writeout to a different directory outside seems to work.

Any specific Windows rights that need to be given to a directory for writeout?

My OS is Linux/Fedora 35.

Without knowing that Feodra is sadly no more officially supported (it used to be the case a few years ago as I was using it on Fedora) I purchased a standalone license of Maple 2021 and  downloaded the Linux installer but am unable to run the file

Maple2021.2LinuxX64Installer.run

from command line (typing 

% sh ./Maple2021.2LinuxX64Installer.run

produces the error "can't execute a binary file") or by clicking on it ("no software installed to run this file").

Before returning the product, I looked at this page to find a possible workaround:

https://faq.maplesoft.com/s/article/Maple-is-not-activating-on-64-bit-Linux?language=en_US

where some tips to install Maple on non-officially supported Linux  os.

I installed lsb packages so that typing:

lsb_relase -a

outputs

LSB Version:    :core-4.1-amd64:core-4.1-noarch:cxx-4.1-amd64:cxx-4.1-noarch:desktop-4.1-amd64:desktop-4.1-noarch:languages-4.1-amd64:languages-4.1-noarch:printing-4.1-amd64:printing-4.1-noarch
Distributor ID:    Fedora
Description:    Fedora release 35 (Thirty Five)
Release:    35
Codename:    ThirtyFive

Anyone has succeeded to install Maple 2021 on Fedora? Thank you in advance.

Simple question

Got stuck

tup_10_g_trying.mw

Want output to look like - 

tuple10(50,12,14,0,0,0,0,0,0,0,0)

1 5 17 19
2 17 29 31
3 29 41 43
4 47 59 61

Please assist.
Regards,
Matt A