How do i go about identifying all horizontal and vertical asymptotes for a given problem?

Lets say (6x^2)/(x^3+2x^2-5x) for example, with multiple powers. How do I identify all of the asmpytotes?

And I was also curious, does every undefined value of f(x) lead to a vertical asymptote? Can the graph of of a function cross the graph of its horizontal or vertical asymptotes, and how many horizontal asymptotes can a graph have?

I need to answer a question, using maple, mathcad, or a similar algebra solver.

I have a little experience in Maple, and thought it would be easy, buts its not, here is the question.

The question is

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Let P and Q be two points in the x-y plane with coordinates (1,2)  and (1,-1) respectively with respect to an origin O. Express OP, OQ and QP in the form Ai  + Bj   where A and B are scalars. Let R be a point on OP so that OR = 1/3OP . Find OR and QR in terms of i  and j .

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I have no idea how to do this.

I need to answer a question, using maple, mathcad, or a similar algebra solver.

I have a little experience in Maple, and thought it would be easy, buts its not, here is the question.

The question is

-----

Let P and Q be two points in the x-y plane with coordinates (1,2)  and (1,-1) respectively with respect to an origin O. Express OP, OQ and QP in the form Ai  + Bj   where A and B are scalars. Let R be a point on OP so that OR = 1/3OP . Find OR and QR in terms of i  and j .

-----

I have no idea how to do this.

I wanted to make an animation of the 3-leaved rose, but the following codes only produce the separate figures.

with(plots):
r:=sin(3*t):

K:=30: for i from 1 to K do ti:=i*2*Pi/K:

curve[i]:=polarplot(r(t), t=0..ti) od:

C:=display(seq(curve[i],i=1..K), insequence=true):

display(C, scaling=constrained,tickmarks=[0,0], thickness=3);

 The following codes produces the animation I needed.
with(plots):
r:=sin(3*t):

K:=30: for i from 1 to K do ti:=i*2*Pi/K:

curve[i]:=polarplot(r(t), t=0..ti) od:

C:=display(seq(curve[i],i=1..K), insequence=true):

display(C, C, scaling=constrained,tickmarks=[0,0], thickness=3);

The only difference is in the last line, where the “C” has been written twice instead of once. I don’t know why. Could anyone explain it to me? Thanks.

    It’s a pity that Maple does not offer easy ways to plot the region between two curves in the xy-plane. The option “filled=true” can only plot the region between the curve y=f(x) and the x-axis.

Maple 11:

I've made a list of all of the elements of the symmetric group s_6:

> S_6 := permgroup(6,{[[1,2]],[[1,2,3]],[[1,2,3,4]],[[1,2,3,4,5]],[[1,2,3,4,5,6]],[[1,2],[3,4]],[[1,2,3],[4,5]],[[1,2,3],[4,5,6]],[[1,2,3,4],[5,6]]});
> ident := permgroup (6, {[]} ):
> cosets(S_6, ident);

How do I extract certain types of cycle structures (e.g (**)(**)) from the list?

Thanks in advance.

I typed in

series( 1/4*sqrt(2)*sqrt(Pi)*exp(-1/2)*(erf(1/2*sqrt(2)*x-1/2*I*sqrt(2))+erf(1/2*sqrt(2)*x+1/2*I*sqrt(2)))*exp(1/2*x^2),x);

I used  exp to avoid a pitfall.

Maple says

A link to a Maple10 worksheet is attached below.  The worksheet has the command lines but has not been executed so it size came under the limit for uploading.  The worksheet is an effort to animate the radius vector to a spacecurve complete with the tangent vector and associated normal and binormal vectors.  Early in the worksheet we suceed in animating the radius vector and the spacecurve.  This success was achieved with some pain.  For instance errors with the plot structures na ddisplay command would not work unless the whole sheet was executed - if, after this,

Hi

I have a system of 33 equations in 33 unknowns. I figured I could use Linear Algebra and Maple to solve this system. Now nearly 9 hours later Maple is still 'Evaluating'. It's been many years since I studied Mathematics and I am very rusty since I rarely use what I learned directly in my job.

Also this is my first attempt at using Maple so please be gentle if you see a ridiculously stupid mistake :-)

Hey,

I am trying to plot 3d graphs but I get the following error message written in blue:

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct.

The function im trying to plot is:

f(x,y)=[ xy (x²-y² ] / (x² + y²)=expr

This is what I write in Maple:

plot3d( expr,x=-1..1, y=-1..1)

In advance, thanks.

Emile

I have a number of expressions.  An example is:

-1/3*(xjm1^2-2*xj*xjm1+xj^2+3)/(xjm1-xj)

I would like to substitue the expression h=xj-xjm1, which in this case would result in

1/h+2*h/6.

Does anyone know how I can make this sort of substitution in Maple automatically?

Hello,

Hopefully, anyone can help me with the following problem:

I have two functions:  Inta=f(Pa) and ETa=f(Pna). Both can not be solved analytically, but I can plot them separately when I use >plot (evalf(Inta), Pa=0..100) and >plot(evalf(ETa), Pna=0..100). So far no problem.

Furthermore, Pna can be described as >Pna:=Pa-Inta, so in fact ETa=f(Pa). But I fail to plot ETa against Pa (or at least it takes ages..since it keeps 'evaluating'..... for days) . I tried several things like:

Hello

When I export maple files into html files (with gif images), I often get jibberish text after "a>b". Maybe it's rendered as a html tag or something, I don't know.

Hiya,
I have an implicit equation;

> tan(beta)=-2/alpha*(beta);

where,

> beta:= sqrt(lambda*alpha-(alpha/2)^2);

for some dimensionless variable alpha.
I want to solve the equation for lamba and plot it as a function of beta.... but I don't know how to go about it.

Thanks for your help
k

So I have read (correctly?) that I can create an object with maple?

How do I go about that?  Just a push in the right direction, im not looking to do anything crazy at this moment, just an object with an array of numbers, some variables also with meaningful information.

Am I headed in the right direction investigating modules?

Thanks!