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align the text in the cells ...

Asked by: jalal 435
March 24 2025
1  6

Hi,

I'm working on formatting my tables for export to PDF. Is there a way to align the text in the cells (to the left, for example)?

Thanks

GenerateSimilar_Ala.mw

why select(has,-a^2,x); returns 1?...

Asked by: nm 11348
select
March 23 2025
2  4

I do not understand why select(has,-a^2,x); returns 1 but select(has,a^2,x); returned undefined.

Should not both return undefined, since there is no x anywhere in the expression?

I looked at help and do not see a clue so far.

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1849 and is the same as the version installed in this computer, created 2025, March 12, 12:37 hours Pacific Time.`

> 

restart;
> 

C:=a^2;
select(has,C,x);

a^2

undefined

> 

C:=-a^2;
select(has,C,x);

-a^2

1

 

 

Download select_question_march_23_2025.mw

Here is another variation, where I changed a^2 to a

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1849 and is the same as the version installed in this computer, created 2025, March 12, 12:37 hours Pacific Time.`

> 

restart;
> 

C:=a;
r:=select(has,C,x);

a

> 

C:=-a;
r:=select(has,C,x);

-a

1

 

 

Download select_question_v2_march_23_2025.mw

The good thing is that has(C,x) returns false in both case. So the problem is not with the has call. It is select which decided to return 1 when there is negative sign. But why?

> 

restart;
> 

C:=a;
r:=has(C,x);

a

false

> 

C:=-a;
r:=has(C,x);

-a

false

 

 

Download select_question_v3_march_23_2025.mw

Why when delete and write take a time to run in wo...

Asked by: salim-barzani 1545
worksheet text editing
March 23 2025
0  8

a lot of time i have this issue when i want delete something it take a lot time to show the in this worksheet it happen too what is issue it is becuase all the text are not in text modde or what? and when i want copy and past my function to place with text is write null for me, what is problem?
and why in end of my display there is two graph?

2-line-label-done.mw

An Introduction to Limits with Maple

by: Paras31 230 Maple 2024
calculus limit
March 21 2025
2  0

LIMITS

Limits in maths are defined as the values that a function approaches the output for the given input values. Limits play a vital role in calculus and mathematical analysis and are used to define integrals, derivatives, and continuity. It is used in the analysis process, and it always concerns the behavior of the function at a particular point. The limit of a sequence is further generalized in the concept of the limit of a topological net and related to the limit and direct limit in the theory category. Generally, the integrals are classified into two types namely, definite and indefinite integrals. For definite integrals, the upper limit and lower limits are defined properly. Whereas indefinite integrals are expressed without limits, and it will have an arbitrary constant while integrating the function.

Sometimes we can't work something out directly ... but we can see what it should be as we get closer and closer!

Example 1

> 

"restart; f(x):=(|x|-3)/(x-3);"

proc (x) options operator, arrow, function_assign; (abs(x)-3)/(x-3) end proc

 (1)
> 

plot(f(x), x = -10 .. 10, discont = true, color = "Green")

 
> 

f(3)

Error, (in f) numeric exception: division by zero

  

Now 0/0 is a difficulty! We don't really know the value of 0/0 (it is "indeterminate"), so we need another way of answering this.

So instead of trying to work it out for x=3 let's try approaching it closer and closer:

> 

f(3.01)

1.000000000

 (2)
> 

f(3.0000001)

1.000000000

 (3)
> 

f(2.9999999)

1.000000000

 (4)
> 

Limit(f(x), x = 3)

Limit((abs(x)-3)/(x-3), x = 3)

 (5)
> 

limit(f(x), x = 3)

1

 (6)
> 

limit(f(x), x = 3, left)

1

 (7)
> 

limit(f(x), x = 3, right)

1

 (8)

Example 2

Sometimes some functions are not continuous. That is, they appear to be approaching two different values when they are approached from two sides.

> 

"g(x):=piecewise(0<x<2,1/(2 x-x^(2)),2 <x<=3,2 -x,3<x<4,x-4, 4<=x,Pi,undefined);"

proc (x) options operator, arrow, function_assign; piecewise(0 < x and x < 2, 1/(2*x-x^2), 2 < x and x <= 3, 2-x, 3 < x and x < 4, x-4, 4 <= x, Pi, undefined) end proc

 (9)
> 

plot(g(x), x = -10 .. 10, y = -1 .. 10, discont = true, color = "Red")

 

Suppose we want to approach 2 and see the function’s limit. This naturally leads to directions from which we can approach. Left-hand side and the right-hand side limits.

The right-hand side limit is the value of the function that it takes while approaching it from the right-hand side of the desired point. Similarly, the left-hand side limit is the value of function while approaching it from the left-hand side.

> 

eval(g(x), x = 2)

undefined

 (10)
> 

limit(g(x), x = 2, left)

infinity

 (11)
> 

limit(g(x), x = 2, right)

0

 (12)
> 

limit(g(x), x = 2)

undefined

 (13)

And the ordinary limit "does not exist".

> 

g(4)

Pi

 (14)
> 

limit(g(x), x = 4, left)

0

 (15)
> 

limit(g(x), x = 4, right)

Pi

 (16)
> 

limit(g(x), x = 4)

undefined

 (17)

And the ordinary limit "does not exist".

> 

with(Student[Calculus1]); LimitTutor()

Example 3

Estimate the value of the following limit limit(h(x)*where, x = 2), h(x) = piecewise(x <> 2, x+12, x = 2, 4).

> 

"h(x):={[[x+12,x<>2],[4,x=2]];"

proc (x) options operator, arrow, function_assign; piecewise(x <> 2, x+12, x = 2, 4) end proc

 (18)
> 

plot(h(x), x = -10 .. 10, discont = true, color = "#40e0d0")

 
> 

limit(h(x), x = 2)

14

 (19)

The limit is NOT 2025!Remember from the first example that limits do not care what the function is actually doing at the point in question. Limits are only concerned with what is going on around the point. Since the only thing about the function that we actually changed was its behavior at x = 2 this will not change the limit.

Example 4

> 

" w(x):=piecewise( x<0,-x+5,x>=0,2 x);"

proc (x) options operator, arrow, function_assign; piecewise(x < 0, -x+5, 0 <= x, 2*x) end proc

 (20)
> 

plot(w(x), x = -10 .. 10, y = -10 .. 10, discont = true, color = "Blue")

 
> 

limit(w(x), x = 5)

10

 (21)
> 

limit(w(x), x = 6, left)

12

 (22)
> 

limit(w(x), x = 1, right)

2

 (23)

Example 5

> 

" k(x):=piecewise( x<5,x+4,x>=5, x^(2)-2);"

proc (x) options operator, arrow, function_assign; piecewise(x < 5, x+4, 5 <= x, x^2-2) end proc

 (24)
> 

plot(k(x), x = -10 .. 10, discont = true, color = orange)

 
> 

limit(k(x), x = 2)

6

 (25)
> 

limit(k(x), x = 5, left)

9

 (26)
> 

limit(k(x), x = 5, right)

23

 (27)
> 

limit(k(x), x = 5)

undefined

 (28)
> 

limit(k(x), x = 6)

34

 (29)

Example 6

> 

restart
> 

" l(x):=piecewise( x<=1,(x-8)/(x-3),x>=3, sqrt(x^(2)+x+2), undefined);"

proc (x) options operator, arrow, function_assign; piecewise(x <= 1, (x-8)/(x-3), 3 <= x, sqrt(x^2+x+2), undefined) end proc

 (30)
> 

plot(l(x), x = -10 .. 10, discont = true, color = "Blue")

 
> 

limit(l(x), x = 0)

8/3

 (31)
> 

limit(l(x), x = 1, left)

7/2

 (32)
> 

limit(l(x), x = 1, right)

undefined

 (33)
> 

limit(l(x), x = 2)

undefined

 (34)

Example 7

Estimate the value of the following limit. limit(H(t), t = 0)where, H(t) = piecewise(t < 0, 0, t >= 0, 1)

> 

" H(t):=piecewise( t<0,0,t>=0, 1);"

proc (t) options operator, arrow, function_assign; piecewise(t < 0, 0, 0 <= t, 1) end proc

 (35)

This function is often called either the Heaviside or step function. We could use a table of values to estimate the limit, but it’s probably just as quick in this case to use the graph so let’s do that. Below is the graph of this function.

> 

plot(H(t), t = -10 .. 10, discont = true, color = "Blue")

 
> 

limit(H(t), t = 0, left)

0

 (36)
> 

limit(H(t), t = 0, right)

1

 (37)

We can see from the graph that if we approach t = 0from the right side the function is moving in towards a yvalue of 1. Well actually it’s just staying at 1, but in the terminology that we’ve been using in this section it’s moving in towards 1.

Also, if we move in towards t = 0 from the left the function is moving in towards a yvalue of 0.

According to our definition of the limit the function needs to move in towards a single value as we move in towards t = a (from both sides). This isn’t happening in this case and so in this example we will also say that the limit doesn’t exist.

 

NULL

Download limits.mw

How remove issue of Float(undefined)?...

Asked by: salim-barzani 1545
user-error
March 21 2025
3  2

i did plot without reducing the decimal but when i reduce to 2 decimal this error is showing up How i fix this issue?
plot.mw

What type of region in my orlsheet?...

Asked by: awass 301
worksheet editing
March 21 2025
0  0

I occasionally find myself inexplicably in a region of my worksheet that does not respond to my editing, fe.g., I cannot erae or I cannot copy. I recently typed a command-there was an error of some form and I tried unsuccessfully to edit it. Then I tried to copy the code and enter it at a prompt. It refused to enter it at the prompt but copied it below the prompt in a strnge region that I do not understand. When I retyped the command at a prompt it worked fine. I do not understand th dead regions that pop up mysteriously. (I am using Maple 2024 on a Mac) The page is too long to copy but I could upload it if given directions.

How do true evaluation for finding unknown?...

Asked by: salim-barzani 1545
parameters algsubs duplicate-question
March 21 2025
3  2

in this equation we have a list of a lot paramter which i have to find it but in prgress to find it some issue are appear i don't know how many term i have to replacing by algsubs there is any way for showing that something like lpring just for factoring and replacing if we did something like that in one step we can replacing all and then find our parameter there is any way for finding parameter like that?

Download pro.mw

How remove sign of integral by substitution?...

Asked by: salim-barzani 1545
substitution pde differential-equations
March 21 2025
3  4

in this integral PDE author did a substitution and the integral is simplify and removing how i can do that as mention in picture i did try but i think need a technique

Download int.mw

Understanding PDEs' Initial Condition Notations ...

Asked by: Paras31 230
March 20 2025
1  6

All three expressions define the same initial velocity condition in different notations.
ic1 := u(x, 0) = f, D[2](u)(x, 0) = g
ic2 := u(x, 0) = f, diff(u(x, 0), t) = g;
ic3 := u(x, 0) = f, u__t(x, 0) = g;  

Why does only ic1 work while ic2 and ic3 do not? Should I use another way?

wave_equation_1D.mw

Change default entry style for execution cells?...

Asked by: studentX369 30
March 20 2025
1  7

Working on updating a very large and out of date guidebook and I need the content of execution cells to be 'Text' for illustrative purposes. It's tedious to constantly have to hit F5 for every, single, new, cell as I'm working through this. Is there a way I can just have the default style be 'Text' instead of 'Math'?  I can't seem to find that as an option anywhere.

Inserting a new text prompt shortcut key?...

Asked by: studentX369 30
March 20 2025
1  3

Ctrl-j/k work fine for inserting a new execution prompt, why doesn't there seem to be a short cut for a new text prompt?  Ctrl+shift+j/k just enters a new line in the current execution prompt.  I'm on Linux using Maplesoft 2024.

How to solve term7?...

Asked by: Alfred_F 305
March 20 2025
1  8

I'm doing something wrong again in the attached file. Please advise.

test.mw

How to lower the plot title? ...

Asked by: C_R 3367
March 19 2025
2  7

Is it possible to reduce the space between the plot title and the 3dplot in the attached file?

Plot_title_too_high.mw

how to help dsolve find this ode solutions?...

Asked by: nm 11348
ode dsolve differential-equations
March 12 2025
1  17

This is problem from INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014 ,  Chapter 2. First Order Equations. Exercises 2.4, page 57, problem 39

Maple 2024.2 can't solve it. But solution is arctan(t)-t*y(t)^2 = 0 which Maple verifies correct

> 

restart;
> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1848 and is the same as the version installed in this computer, created 2025, March 11, 16:9 hours Pacific Time.`

> 

restart;
> 

ode:=(1/(1+t^2)-y(t)^2)-(2*t*y(t))*diff(y(t),t)=0;
IC:=y(0)=0;

1/(t^2+1)-y(t)^2-2*t*y(t)*(diff(y(t), t)) = 0

y(0) = 0

> 

sol:=dsolve([ode,IC])

> 

mysol:=arctan(t)-t*y(t)^2 = 0;

arctan(t)-y(t)^2*t = 0

> 

odetest(mysol,[ode,IC])

[0, 0]

 

 

Download can_not_dsolve_march_12_2025.mw

Any one has suggestion how to help dsolve find this solution?

Why does Maple not understand the interval [1,1] a...

Asked by: Saalehorizontale 55
solve interval simplification
March 12 2025
2  4

Hey guys, 

I am solving many systems of polynomial equations. Sometimes I get the same solution, just in a diffrent are, so for example the first solution is for y between 0 and 1 and the second solution is for y between 1 and 2. So now I want to take those solutions intervals and combine them so I can make one solution out of two. However I am struggeling with working with intervals in Maple. It is not that easy how I expected it to be.

I wrote an own program which works quite nice unless there is a single solution which would meen an interval like [1,1] meaning y=1working_with_intervals.mw

> 

restart; sets := [{1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]; intervals := [RealRange(Open(1), Open(infinity)), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]; correct_form := [y::(RealRange(Open(1), Open(infinity))), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]; Sol := solve(`~`[convert](Or(op(correct_form)), relation))

[{1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]

  

[RealRange(Open(1), infinity), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]

  

[y::(RealRange(Open(1), infinity)), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]

  

RealRange(Open(0), Open(1)), RealRange(Open(1), infinity)

 (1)
> 

restart; sets := [{1}, {1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]; intervals := [[1, 1], RealRange(Open(1), Open(infinity)), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]; correct_form := [y::[1, 1], y::(RealRange(Open(1), Open(infinity))), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]; Sol := solve(`~`[convert](Or(op(correct_form)), relation))

[{1}, {1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]

  

[[1, 1], RealRange(Open(1), infinity), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]

  

[y::[1, 1], y::(RealRange(Open(1), infinity)), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]

  

RealRange(Open(0), Open(1)), RealRange(Open(1), infinity)

 (2)
 

NULL

Download working_with_intervals.mw

In the attached file you can see my problem. When I add the intervall [1,1] the solution should become (0,infty), but it seems like Maple does not understand what I mean by [1,1], so the 1 is not part of the solution "Sol".

FYI: I wrote a program which is able to convert "sets" into "intervals" into "correct_form" using RealRange, but it is not necesarry for my problem. 

So my questions are: Why doesnt Maple recognize [1,1] as an interval containing only the 1? Is there a way I can rewrite the intervall so I can use it for the solve process in "Sol"? I also thought about making two diffrent sets with the same intervals than adding [1,2) to the one set and (1,2) to the other set and than make an intersection but I seems to be very complicated for a seemingly easy problem. Is there a easier way to work with intervals? 

Regards and thank you

Felix

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