Items tagged with calculus



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



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


VectorCalculus[diff] does not do what I want.






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.



Why does:


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:


in order to receive the answer 



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:







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





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);


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).



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

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

[0, exp(-1/2)]



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?



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...

The Single Variable Calculus Approximate Integration Tutor (and the function ApproximateInt) work fine for the built-in example of sin(x) from 0 to Pi.  But if you change it to sin(Pi*x) from 0 to 1 then plot options are ignored.  And if you ask to integrate sin(3.1415926*x) from 0 to 1, then it works again.  Is there a work-around?

I got Maple 17 a few weeks ago and it has been helpful in my learning of calculus, but not as much as I had hoped.


I also bought the Calculus study guide which is a big disappointment. For example, I tried using the integration methods tutor for the integral  cos(5x).

The correct answer is  1/5 sin(5x) + C and is found with U-substitution. 

With the tutor, I entered cos5x into the function box.  cos(5x) does not work....

How to solve with maple using integration by parts the integral?int(sec(x)^(n),x);
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