Items tagged with calculus

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);

Can someone please solve only #19 and #25 using Nwton's method in Maple. I really appreciate it.


The questions are attached. Thank you

You have been asked to design a one-liter can shaped like a right circular cylinder. What dimensions will use the least material?

-I really need help on how to correctly plug this into my computer. Thank you in advance.


The command

f := -.1*(x+3)*(x-1)*(x-3.5):


produces different results in Maple 13 and Maple 16.02.

In particular, the concavity=[] option seems to be ignored in 16.

Also, it may be my imagination, but execution seems slower in 16, but I didn't try timing it.

My apologies, if this has already been noted.


So far, my math group has the entire roller coaster plotted using spacecurves on a 3D plot on Maple. The only issues is now we need to take the derivative between the different sections we created in order for there to be no corners or spaces; basically to make sure the "coaster" runs smoothly.

We get how to do it on paper but we're running into some difficulty doing it on Maple. My question is, how the heck do we do what I just said we wanted to do.

I'm looking for several challenging projects for a Calculus II course using Maple which I'll be teaching in Spring 2013.  By challenging I mean that the project will have several steps including both conceptual and computational aspects.  I'd also like them to be suitable for group work if possible.  I'd be willing to devote from 3-5 class periods for each of three or four different projects.  Our Calc I and Calc II are five hour...

Can somebody, please, try this command in Maple 16 (or at best Maple 16.02)?


In Maple 15 I get the graph in about 1s, however in Maple 16.02 it loads about 20s and it is even not as perfect as is in Maple 15. Furthermore, when I try to evaluate


it says that it lasted only 1-2s. There is some problem...







Hi all,


After I loaded the package with(VectorCalculus), the output of vectors changed to a different one.

Is there any real "difference" when...

We have just released Teaching Calculus with Maple: A Complete Kit.  Leveraging both Maple and Maple T.A., Teaching Calculus with Maple includes lecture notes, student worksheets, Maple demonstrations, Maple T.A. homework, and more – everything you need to teach Calculus 1 and Calculus 2.  Teaching Calculus with Maple  was developed at the University of Guelph under the leadership of an award-winning teacher and field-tested in classes with hundreds of students.

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