Download Maple_primes_ques_27.mw

I'm in the process of reviewing Calculus for self-learning--I'm not in a class room but learning/re-learning on my own. Would the Calculus Bundle be sufficient for that purpose? Does it contain enough supporting information to permit self-learning? Would steps be shown for equation solutions?

A new edition of Maplets for Calculus (M4C) is now available. M4C v1.3 is a collection of 129 maplets for calculus students and instructors. The 35 new maplets fill in some gaps in the coverage of precalculus and single variable calculus and begin to address multivariate topics. Each maplet provides a customized graphical user interface (using 2D and 3D graphics and animation) to provide immediate, step-by-step guidance through an endless supply of random ...

with the following input:

with(VectorCalculus);

X := r -> sqrt(2/Pi)*alpha*exp(-alpha^2*(r.r));

a_0:=a*<1/(2*sqrt(3) , 1/2>;

r:=<x,y>;

K:=<k_1, k_2>;

assume(alpha::real);

assume(alpha>0);assume(k_1>0);

assume(k_2>0);

assume(k_1::real);

assume(k_2::real);

eq1:=int( X(r-a_0) , x=-infinity .. infinity);

Why is the ouput :

In a recent blog post, I pointed out that Maple did not have a built-in functionality for drawing graphs that arise in computing volumes by slices. However, I did provide several examples of ad-hoc visualizations that one could build with the graphing tools in Maple.

Recently, a user called attention to a weakness in the Student Calculus 1 command, VolumeOfRevolution. This command (and the tutor built on it) will draw a surface of revolution bounded by the surfaces generated by revolving the graph of one or two functions.

How could develop the following in Maple:

1) Solve the series using the alternating series method:

12 - 6 + 3 - 1.5...

I know the answer is 8 because it is in the back of my calculus textbook...I just don't know how it is 8.

2) Solve the series: ((2/k) - (2/k+3)) where k = 1 to infinity.

I know the answer is 11/3...I just don't know how to get there.

My question is this:

In with(DifferentialGeometry): with(JetCalculus) with(Physics):

I work with the following Jet Bundle:

DGsetup([x], [u, psi], E, 40),

where psi is declared anticommuting with Setup(anticommutativeprefix={psi}).

When I work with expressions that are differential polynomials in u with coefficients arbitrary functions of u, the EulerLagrange operator behaves correctly. The same is true if I multiply these expressions by psi or by psi_1 ...

Could the Student:-Calculus1:-Hint routine detect that its answer(s) will result in an endless cycle (even if only cycles of length 2)? Maybe it could check, and not make such hints?

Below is just one example. Sure, its hint is not great here, due to which this is not a fantastic example. But I'm still wondering about cycling prevention for Rule&Hint in general.

This is Maple 13.01.

> restart: > with(Student:-Calculus1): > Int((x^2+a...

Im using maple 13

I always encounter an error everytime i use the feature ShowSolution

the error says:

"Error, (in Student:-Calculus1:-ShowSolution) input expression does not have any incomplete calculus operations"

This always happens in all the calculations.

How should I use the ShowSolution properly?

I am attempting to get MAPLE to generate indefinite integrals that are of the form:

exp(-k[r^2-a^2*cos(x)]^0.5)

from fundamental calculus principles I might set u = [r^2-a^2*cos(x)]^0.5 which then should yield du/dx = 1/2*(a*sin(x)/[r^2-a^2*cos(x)]^0.5).

Then if my math is correct the result should end up:

2*(r^2-a^2*cos(x)]^0.5)*exp(-k[r^2-a^2*cos(x)]^0.5)/[-k*a*sin(x)]

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