## asymptotic...

I want to obtain an asymptotic formula (n->infinity) for

sum(2/k,  k=1..n).

Direct method does not work. Probably it is needed some transformation (maybe theory) before it. Could you help me?

Sandor

## matrix of bits...

alright, heres my newest task that should be easy that has given me nothing but problems.... I have a function, sFunction, that takes in something between 0 and 15 (*only* integers) and spits out a single value. I would like to create a matrix of the output's bits. Since my numbers are 4 bit, that means it should be 4 wide and 16 high. To get the bits I'm planning on BitAnd-ing them with a power of 2 to isolate it. I keep getting "too many levels of recursion" errors on all my attempts.

## question about plot two variables...

Hi, all

I got qeustion about how to 3D plot a function with different values of on parameter.

For example, a  function

y = 2x /(x-m)

m is parameter.

I want to plot the different function curve of y in 3D when m has different values as such m=1, m=5,m=10....

say, y1 = 2x/(x-1)

y2 = 2x/(x-5)

y3 = 2x/(x-10)

btw,  I know how to plot 3D,  but I just want to plot the function at several specific m values.

## Find Maximum...

Hello, If you have an aperiodic function that attains a maximum at some later time say tau, what command in maple would allow you to find it? Mathematica, as far as I know, is only limited to specifying where you think the greatest maximum might be and the only alternative to automate this would only find the first maximum not the greatest maximum.

## view entire matrix, by default?...

Any chance this is possible? I dont like having to 'browse' every time and my matrices arnt even that big. Thanks

## trouble with roots...

Hi, i want to find the roots of a polynomial and replace pepetitive (long) expressions in it by using alias.

solve(x^3+2*x+1=0,x);

-1/6*(108+12*177^(1/2))^(1/3)+4/(108+12*177^(1/2))^(1/3), 1/12*(108+12*177^(1/2))^(1/3)-2/(108+12*177^(1/2))^(1/3)+1/2*I*3^(1/2)*(-1/6*(108+12*177^(1/2))^(1/3)-4/(108+12*177^(1/2))^(1/3)), 1/12*(108+12*177^(1/2))^(1/3)-2/(108+12*177^(1/2))^(1/3)-1/2*I*3^(1/2)*(-1/6*(108+12*177^(1/2))^(1/3)-4/(108+12*177^(1/2))^(1/3))

This looks nasty, so i want to replace (108+12*177^(1/2))^(1/3)

alias(alpha=(108+12*177^(1/2))^(1/3));

## Solving cubic polynomial...

Given a cubic, x^3 - c*x +16=0, I need to find values of c so that the real parts of the complex roots are negative.  Any suggestions?

## Antiderivatives...

Hi, This is my 1st try with Antiderivatiives using Maple 12 Student Edition. These statements work fine and the answers are the same as the book. int(15*x^4-cos(x)+5, x); int(8*x^3+Pi*cos(Pi*x), x); but the below doesn't work. Maple just repeats it with the Integral symbol before it and 'dx' after it. by hand the answer is 3x^(5/3)+x^(3/5)+C. int(5*(x^2)^(1/3)+3/(5*(x^2)^(1/5)), x); thanks

## Approx procedure...

Hi. I have to create a procedure Approx with the procedure call Approx(f, a, b, N). I don't really understand how to write procedures so I'm confused.  The point of the procedure is to return the floating point value of the right Reimann sum SN  which approximates the area under the curve y = f(x) over the interval [a, b]. I don't know where to go from here. Here is what I have so far:

## How to take Fourier Transform of log(t)/t ?...

Hi,

I have difficulty in taking fourier transform of a function f(t).

The function f(t) is not integrable. Through analytical analysis, f(t)
behaves asymptotically the same as a*log(t)/t

for t-> +infinity; and f(t) behaves asymptotically the same as b*log(-
t)/t

for t-> -infinity; where "a" and "b" are some constants.

Is there a way to work around this difficulty and get some sort of
fourier transform of this function f(t), possibly

## A question about procedure...

Hi Everybody,

Suppose I have this procedure assign to p:

>p:=MyProc(args1,args2,args3,h) statement end proc:

where h is the step size.

args1 = {ode,ic} , args2 = x(t) et args3 = t=a..b.  The output of MyProc is a list of list

I would like to do what dsolve do when you write:

p:=dsolve( {ode,ic},x(t),x(t),numeric)

and then evaluate p(2) for example.

## error plotting piecewise function...

Hello I'm trying to plot a piecewise function, only I think the plot I get is wrong. It looks like a linear function when it should be a bit more 'scattered' looking. It also goes past 900 when its max should be 63. Did I mess up the function? Plot arguements? Thanks > pLayer := proc (x) options operator, arrow; piecewise(1

## Maple returning wrong answer...

Hello everyone,

I'm having a little trouble getting Maple to return a correct solution.  It's a simple equation, really, involving the relation of the period of an object around the sun and it's semi-major axis.  Specifically this involves Halleys comet.

Given that halleys comet takes 76 years to complete an orbit.

I set

restart;

eq1:=P^2=(4*Pi*a^3)/(G*M);

and convert P to seconds

P:=convert(76,units,year,second);

G:=6.672e-11;

M:=1.99e30;

solve(eq1,a);

## How do I make full simplification of expressions?...

I am using Maple 12.

I often try to simply expressions, but I found that very often I must manually guide the simplification procedure.  For example a result from inverse laplace trasformation is:

Ssi(t)+pi/2

But this, by definition, equals Si(t).

However, the function simplify doesn't work for such a purpose.  Also in many other cases the function 'simplify' don't work without human guide.

## How could i calculate the following equation in Ma...

when i calculate the equation as:

solve({g*(w-c)+(1/4)*(a-g*w+g*r)^2/(b*(p-k))-(a-g*w+2*g*r)(a-g*w+g*r)/(2*b*(p-k)) = 0}, {r})

i got the message "Warning, solutions may have been lost" without any feedback,

does the equ too complex to calculate in Maple? or i make some mistakes?

how should i do to solve this equation~

ths

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