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I under stand how to do the calculus that's easy enough, but Maple is stil giving me a hard time.  The math par t is let the radius of the cylinder be r cms. 0<r<10 Then the height is 2 * Sqrt 100-r^2, the volume is V(r)=2PIr^2* sqrt 100-r^2 cm^3

Differentiante V(r) with respect to r we get V' (r) =2PIr^2(1/(2*sqrt(100-r^2)))(-2r) + (2PIsqrt(100-r^2))(2r)

V'(r)=(-2PIr^3 +4PIr(100-r^2))/sqrt (100-r^2)      V'(r)=2PIr(200-3r^2)/sqrt 100r^2         to find the critical point find the value of r when V(r) =0     2PI(200-3r^2)/sqrt 100-r^2 =0   2PIr(200-3r^2) = 0   r(200-3r^2)=0 

r=0 or 200-3r^2 =0     r=0 or r^2=200/3 r=sqrt(200/3) =10sqrt(2/3)   r is not in the interval so ignore it.  The critical point for 0<r<10 occurs at r = 10sqrt(2/3)       Since V'(r) >0 for 0<r<10sqroot(2/3) and V'(r) <0<10sqrt(2/3)<10

The dimensions are r=10sqrt(2/3) =8.16 cm and h=20/sqrt3 = 11.55 cm the volume is 4000PI/3*sqrt3=2418.4 cm^3

So how do I translate this into maple? Any help is greatly appreciated.

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Creating Questions in Maple T.A. – Part #1

This webinar will demonstrate how to create questions in Maple T.A., Maplesoft’s testing and assessment solution for any course involving mathematics. The presentation will begin with an overview of the basic types of questions available, and then delve into how to create various types of questions in Maple T.A. Incorporating algorithms and feedback directly into questions will also be touched on. Finally, the session will wrap up with an explanation and several examples of how to create better questions using the question designer.

This first webinar in a two part series will cover true/false, multiple choice, numeric, mathematical formula, fill in the blank, sketch, and FBD questions. A second webinar that demonstrates more advanced question types will follow.

To join us for the live presentation, please click here to register.

Clickable Calculus: Linear Algebra

In this webinar, Dr. Robert Lopez will apply the techniques of “Clickable Calculus” to standard calculations in Linear Algebra.

Clickable Calculus, the idea of powerful mathematics delivered using very visual, interactive point-and-click methods, offers educators a new generation of teaching and learning techniques. Clickable Calculus introduces a better way of engaging students so that they fully understand the materials they are being taught. It responds to the most common complaint of faculty who integrate software into the classroom – time is spent teaching the tool, not the concepts.

To join us for the live presentation, please click here to register.

Hi all,

I am stuck with the following problem:

convert(cos(alpha), exp); works fine for me.

Once I have the trigonometric functions in a matrix, it does not work any more:

In the latter line, A keeps the trigonometric functions. Why is this the case? Is there any way to force maple to keep the complex exponentials instead of trigonometric functions?

 

I am using LinearAlgebra and VectorCalculus.

 

Best Regards

Wassja

f:=x+y+y;

diff(f,x);
diff(f,y);
diff(f,z);

What I hope to get is a vector with i-th entry being the dervative of f, differentiated w.r.s.t the i-th parameter, like this

Vector([1,1,1]);

 

Is there a more efficient (built-in) command to do this?

 

VectorCalculus[diff] does not do what I want.

 

Thanks,

 

casper

 

We have just released an all-new, second edition of the Calculus Study Guide.

This guide has been completely rewritten and greatly expanded and to take full advantage of Maple’s Clickable Math approach.  It covers all of Calculus I and Calculus II and has over 450 worked examples, the vast majority of which are solved using interactive, Clickable Math techniques. 

Not only is this guide useful for students learning calculus, but it can also serve as a guide for instructors interested in pursuing a syntax-free approach to using Maple in their teaching.

See Clickable Calculus Study Guide for more information.  For even more information, you could also attend a live webinar about the new study guide next Wednesday.

 

eithne

Why does:

Student[Calculus1]:-Tangent(tan(3*x)-5*exp(-x^3),x=0,output=plot,gridlines=true,caption="")

produce the following error?

Error, (in plots:-display) integer or integer range expected in op list

I was required to purchase Maple 17 for my upcoming Calculus III course, and until now, I have been using my TI-Nspire CAS CX for all of my CAS needs.  I am going through various tutorials/labs in an effort to learn how to use the Maple 17 Software. As a part of this process, I am attempting to solve a system of equations and was told to use the following command:

>solve({2*x+3*y=7,5*x+8*y=9},{x,y}); 

in order to receive the answer 

{y=-17,x=29}.

 

Instead, I have received the following error message, which has no help attached to it through the help page.

solve({2*x+3*y = 7, 5*x+8*y = 9}, {x, y});
Warning, solving for expressions other than names or functions is not recommended.

I am hoping this has something to do with Mac vs. Windows software, and that it has a simple solution.  I would greatly appreciate any guidance!

I'm taking calculus and my professor introduced us to maple software. The professor asked us to plot the families of curves for this orthogonal equation:

dy/dx = (x^2) - (2y^2) - C = 0

This is what I had so far:

 

restart;

with(DEtools):

with(plots):

 

Function:=unapply(simplify(x^2-2y^2-C),(x,y)):

'Function'(x,y) = Function(x,y);

plotFunction:=C->implicitplot(eval(F(x,y),a=C),x=-5..5,y=5..5,scaling=constrained):

plot1:=display(seq(plotFunction(a),a=-5..5)):

display(plot1);

 

This is only display one family. How do I code for it plot the other families?

(The graph should look like curves converging from left, top and right sides toward to the origin of the axes)

Please help.

How can I expand the mutivariate taylor series of the functions below about the point (x,y)

f(h*a[2]+x, h*a[2]*k[1]+y);

 and

f(h*a[3]+x, y+h(a[3]-b[32])*k[1]+h*b[32]*k[2]);

I copied and pasted this from the example page and I have to get this same graph for an assignment

im using maple 17

 

Tangent(x^3-x, -.432, view = [-2 .. 1, DEFAULT], output = plot)

 

when i hit enter the return was

 


Tangent(x^3-x, -.432, view = [-2 .. 1, DEFAULT], output = plot)                       (1)

 

Hello All,

I have had a few questions that have come up while working on a Maple Assignment for my Calculus III class. I was wondering if anybody could help me with these questions, as well as show me how to enter them in Maple. Here are the questions I have been struggling with.

 

  1. In the xy-plane, graph the ellipse ((x-4)^2)/(4))+(y-4)^2=1 and two level curves of F(x,y)=x^3+y^3-3xy that just touch the ellipse.

                  a. What do we know about the gradients of F and the ellipse at those points?

                  b. Use your graph to approximate the minimum and maximum values of F subject to the constraint ((x-4)^2)/(4))+  (y-4)^2=1.

 

      2. A company manufactures a product using inputs x,y,z according to the production function Q(x,y,z)=20x^(1/2)y^(1/4)z^(2/5). The prices per unit are $7 for x, $12 for y, and $18 for z.

                 a. Create the cost function

                 b. The company wants to produce 2500 products. Estimate the minimum cost by using the graph of the level surfaces of the cost function (from part a) together with the production constraint.

Any help you could give me would be much appreciated. Thanks!!

 

 

            

I'm trying to use the CriticalPoints command from the Student[Calculus1] package to determine the critical points of f(x) = x^2 * ln(x).

 

with(Student[Calculus1]):

f := proc (x) options operator, arrow; x^2*ln(x) end proc:

`assuming`([CriticalPoints(f(x))], [x > 0])

[0, exp(-1/2)]

(1)

``

My issue is this. A critical point is defined as a value of x in the domain of f(x) where either f'(x)=0 or f'(x) does not exist. Clearly x=0 is not in the domain of f(x) = x^2*ln(x). How may I "trick" Maple into returning only the value exp(-1/2)?  As seen above, my attempt to use the assuming command proved futile.

More troubling, however, is whether or not the CriticalPoints command is using the correct definition to compute critical points. Can anyone shed some light on this?

 

Download critpts.mw

A sequence of real numbers a_1,a_2,a_3....... satisfies a_0=1 and

How would one go about making a table of variable values for a multivariable equation? By that I mean, lets say you have the equation x-3y+z=5. It can easily be plotted as a plane but what if I wanted to produce a list of key values so I could make a graph myself? Similar to how the TI's can make a table for single variable equations. I ask because I am tasked with making a pencil and paper graph and it would be nice if I had a table that were say, incremented by x=1. Is there...

If I have spreadsheet data, x and y (velocity and time), I need to find distance.  I see numbers of ways to do this, however, I wonder what people would suggest as the fastest / easiest way.  I'm not needing a function really, just results.  Does Maple have tools to simplyify this process, and if not, what process(s) might yield results of determinable or selectable accuracy.  I will have many sets of data in the future that need to be manipulated...
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