## How do i prove limits of functions?...

​​​​​​use epilson- delta definition of a limit to prove that

Limit as x approaches 5 of 1/x =1/5

## geom3d - intersection of two lines - bug?...

There seems to be a bug: in some of the cases, the intersection command works, in others it doesn't.

I'd appreciate any hints as to why this is the case.

intersection_of_two_lines.mw

## simple Question, Elements of a List...

Hello,

I think its a simple question and I hope, someone can help me. For Example:

I have a list of numbers ("M") and I want to write these numbers in a new List but with the restriction

if x<Mthen Mi*2
else Mi

Can someone explain how to solve this in maple?

Thank you very much.
Maritn

## Maximum cylinder in a box: "straw in a box" or act...

I am looking for a pragmatic solution to the question: Can my rolled carpet fit inside a given cardboard box?

It is the (generally unsolvable) problem "straw in a box":

...with the restriction that the cylinder is aligned along the spatial diagonal.

So the application is this:
Is it possible to put a 120cm long rolled (radius 10cm) carpet inside a cardbord box of (inner) dimensions 118cm x 58cm x 38cm ?

Maple code would be perfect, but I have very little Maple experience so I cannot even provide any attempts/code at this stage.

Thanks!

## Calculation of double square root...

A Happy New Year, people in mapleprimes,

I have a question, but this might be an inappropriate question to this site.

In Introduction to Maple, there is a calculation with a double square root.
Related to it, I want to calculate the following expression, which has a value of zero.

`-3*(sqrt(10+4*sqrt(5)))+sqrt(50+20*sqrt(5))+sqrt(10-4*sqrt(5))+sqrt(50-20*sqrt(5));`

Is there any way to use maple  so as to explain how the above expression takes the value of zero?

On earth, I cannot understand why this takes zero.

I hope you will give me a hint.

## How do I extracting values from RootOf ...

I am trying to assess stability from real roots of Eigenvalues that are returned in the RootOf from. I tried allvalues(), evalf() both return the same RootOf list. If memory serves me correctly any square matrix should have and Eigenvalue solution.

Any suggestions?

D curve PointsPoints

PSS

 (1)

## Find an integer...

Dears,

Consider the problem min{|a+2*i| : i integer}, where a is a number of the form 2k*t for a fixed integer k>1 and t in [0,1]. A simple checking shows that i must belongs to the interval [-(1+a)/2,(1-a)/2] and as the legth of this interval is 1, there is two integers in this interval.

How can I compute this integer i with Maple? The commad "ceil" not seem very suitable. Some idea?

## Matrix Palette not working...

At the beginning of my work sheet I used the matrix palette to create several matrix. Now when I try to use the palette this is what I get.

`Matrix(2, 3, {(1, 1) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("1"), Typesetting:-mo(","), Typesetting:-mn("1"))), (1, 2) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("1"), Typesetting:-mo(","), Typesetting:-mn("2"))), (1, 3) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("1"), Typesetting:-mo(","), Typesetting:-mn("3"))), (2, 1) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo(","), Typesetting:-mn("1"))), (2, 2) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo(","), Typesetting:-mn("2"))), (2, 3) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo(","), Typesetting:-mn("3")))})`

To get a matrix from the palette I have to create it on a new worksheet and cut and past it into the existing work sheet.

What is happening?

## Surface Area and Volume...

Hi, I am a Maple newbie. My problem is I do not know how to generate the result to find the answers of these question:

1. a)   Sketch the surface area of the part of paraboloid z = x2 + y2 that lies under the plane z=8.

b)   Compute the surface area.

1. a)   Sketch the solid that lies above the cone z = (x2 + y2)1/2 and inside the sphere x2 + y2 + z2 = 16.

b)   Compute the volume of the solid.

It is possible to calculate these question? Does anyone has a suggestion? Thank you.

## Solving a system of equations ...

Hi all,

Please help me to get a solution for all the desired data in the attached file. As you could see through it, just for 4 out of 20 desired Br, there are answers by the command:
Notice that If I write Br= -7.0 there is no solution, but I wrote Br= -6.999999, and the solution was achieved simply; just by applying an approximation value for '7'.

I don't know why for other data there are no solution...

Best

System_of_Equations.mw

## how to solve non-linear equation?...

restart;
with(PDETools);
diff(r(t), t)-(diff(a[3](t), t))*r(t)/a[3](t)+a[1](t)*p[3](t)-3*r(t)*r(t) = 0;

dsolve(diff(r(t), t)-(diff(a[3](t), t))*r(t)/a[3](t)+a[1](t)*p[3](t)-3*r(t)^2 = 0, r(t));

## how to see all steps of solution in maple?...

how to see all steps of solution in maple? for eg: any second order differential eq.

## how to solve optimal system?...

how to solve optimal system of vector   fields in lie theory in maple?

## Trying to draw a sequence of triangles for animati...

Am trying to draw a series of triangles for animation.  I try to construct the triangles in a loop using:

triangle(cat(T1,`a`),[A,B,C]):

so that the names of the triangles are meant to beT14, T15, T16

I have tried unsuccessfully to use the plots and draw commands ie

draw({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

plots[display({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

Can the animation be done in either?

It seems to want a variable in a list/set format - How do I set that up?  Any comments, or help gratefully received.  The program is below.  Part of the output does give triangles - but they all seem identical:-(

restart:

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

# Altitude exploration  program

#Trying to draw a sequence of triangles for animation

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

with(plots):

with(geometry):

for a from 4 to 6 do

b:=a+1: c:=a+2:

angA:=arccos((a+5)/2/(a+2));

point(A,0,0),point(B,c*cos(angA),c*sin(angA)),point(C,a+1,0):

tabl[a]:=triangle(cat(T1,`a`),[A,B,C]):

printf("a=%d\n",a);

triangle(cat(T1,`a`),[A,B,C]):

end do:

for i from 4 to 6 do

draw({seq(tabl[i], i=4..6)}, scaling=constrained);

printf("a=%d\n",i);

end do;

print(`After do`);

draw({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

Warning, the name changecoords has been redefined

Warning, the name arrow has been redefined

Warning, these names have been redefined: circle, ellipse, homothety, hyperbola, line, point

a=4

a=5

a=6

a=4

a=5

a=6