Integral calculus and differential 1...

==> Integral calculus and differential 1

Question: Being given the function f (x) =1/(3x+1),

a) By using the definition of the derived function (and not the rules of derivation), determine f' (x).

b) Determine the slope of the tangent to the curve of f (x) at the point (1, f (1)).

Instructions: You must use Maple 12 and show your calculations.

Thank you for the assistance offered with these forums.

Randomness

by: Maple

Recently, I was reading about random.org again.  It is an online random number generating service that uses atmospheric noise gathered from radios tuned between stations as a source of randomness.  It has been running more or less continuously for about ten years.   On their analysis page there is a nice pair of bitmaps (scroll down past the Dilbert comic) that contrast their random bits with those from one version of the PHP rand() function. Basically this demonstrates how easy it is to create a pseudo-random number generator that is periodic with too small of a period.

I decided to take a look at Maple's random number generator in comparison.

missing results when solving 3 equations with 3 va...

Hello,I'm trying to solve system of 3 equations for a problem of using Larrange Multiplier

> e1 := 3*x^2+3*y-a*(2*x-6);

3 x  + 3 y - a (2 x - 6)
> e2 := 3*y^2+3*x-a*(2*y-6);

propagation of a virus...

In order to prepar an exam, i would like to discuss about how virus spread.

I got some informations about different models, such as SI, SEI, SIR, MSEIR... and their differentiel equations

But i have some troubles to write and solve them.
i would like to use maple to modelize this propagations, but i don't know how to do at all.

Could someone give me a base, for a quite simple model such as the SI model?

Thanks

Euler-Lagrange...

I have the following functional:

base change for orthogonal polynomials...

```I am looking for the following: given Chebychev polynomials T up
to degree n I want to express them as Legendre polynomials P.

For example one can use OrthogonalSeries[ChangeBasis] for given n.

My question is: can one give/describe/generate/... the transform
matrix for the bases directly?

The intended use is for n <= 512 (or considerably smaller), the
special case T ---> P would be enough for me.

Certainly this is classical, but I can not find it out (or looking
it up).
```

Expressing a moment with units of Nmm, not joules....

For structural engineering problems, when I multiply a force (N) by a distance I generally want the answer in (Nmm) or (kNm) or units of that form.  Yet Maple simplifies the result to Joules, which doesn't mean a whole lot to me when I'm trying to find stresses and strains in structural members.

My question is, how can I define my own set of units that I'm comfortable with instead of having to accept the default Maple units?  I'm not having a lot of success customising units with Maple.

Maple Function...

write a maple function which takes a 2xN matrix and plots the points given by its columns on a 2D graph?

Array of functions...

Hey altogether,

how can I solve the following problem:

for i from 1 to n do f_i := x -> i; od;

In this case f_1(x) should return 1, f_2(x) should return 2, and so on? The code above is not working because the right-hand side is not evaluated. Even trying eval/unapply/.. didn't help.

Stefan

taylor expansion...

Good morning,

I have the following question. I write the following command

t1 := taylor( sin(x), x=0, 6);

How may I plot "t1" excluding  the term O(x^6)?

plot( t1, x=-3..3) does not work -probably- because O(x^6).

JJ

Plotting Probability Distribution...

I need to plot the probability distribution function

f(x) = n!/(x!*(n-x)!*(2^(n))).

Can I just plot this as any other function using the various plot commands, or is there some statistics package option specially made for this?

Also can this distribution help me answer the question of obtaining the probability that the fraction of heads for 10, and 100 total coin tosses will be between 0.445 and 0.555?

Extracting an element from a table-urgent help nee...

Hi, I'm very,very new to maple, project due on monday so help needed urgently please! I have an array (as a result of dsolve) of the form below (obviously a lot longer) [a=0.001, b=123, c=345, d=565] [a=0.002, b=124, c=345, d=567] [a=0.003, b=125, c=456, d=765] I need to plot the first and third columns against each other so I used the op function to extract these columns arr := Array[1 .. 100]; for i to 100 do arr[i] := [op(1, ans(i)), op(3, ans(i))] end do However, this gives me [a=0.001, c=345] [a=0.002, c=345] [a=0.003, c=456]

Differene between two functions...

Hello All,

This is my first post, and I want to thank you for helping guys like me.

I am working on a project, but I've gotten to a point, where I need help :(

Actually, it is 2 points...

• I am using Maple 12 (document mode), and I'm trying to get the following graph drawn:

mm:=(101/100)*ln(10)-ln(S(t))+10-S(t) = 5*t

plot2:=implicitplot(mm, t = 0 .. 10, S = 0 .. 10)

display(plot2)

Function of Functions...

How do I define a Function of functions with maple?

For example:

F(y(x),y´(x))=y(x)*y´(x).

or

F(u(x),v(x))=sin(u(x)v(x)).

Thanks,

Sebastián Varas K.