Axel Vogt

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17 years, 229 days
Munich, Germany

MaplePrimes Activity

These are answers submitted by Axel Vogt

1/12 + arbitrary constant is still an arbitrary constant

Your command says "cut at +-5 for the y-axis"

Try: plot((x^3 - 4*x^2 - 9*x + 36)/(x^3 - 9*x),  x = -3 .. 3);


It seems to dislike floating point numbers.

L:= convert(x2[1], rational);
numboccur(L, 0);

It is non-negative, but not strictly positive. You may look at

minimize(exp(x)+exp(y)+exp(z)+2*exp(-x-y-z), location);

I am rusty on this - but error 53 refers to run time libraries, so it is *.DLL and not *.xla


PS: you do not really want to post 2 very different questions in just 1 thread.

This is more a question of Numerical Analysis, you may start at (which also mentiones the method suggested by Corless)

Using vv's suggestion to sum up over smaller intervals I get
0.005295 - 0.0009968*I for n=0 and 0.7493 - 0.4808*I for n=1
for epsilon = 1e-4.

My machines needs about 1.5 h for each case.

Find attached a solution using the NAG routines which gives
it in about 20 seconds for each case, giving the same figures.

Likewise you write down the recursion function in Cents and finally express it in USD

B:=proc(m::nonnegint) # compute in Cents
round( B(m-1)*(1 + 0.0775) + 400000 );
end proc;
B(0):=400000: # initial

B(30)/100.0; # Cents as USD



Writing as iterated integral and handling s first I get
-0.331842471004086e-3 and -.663684942008173e-1

Edit: I have not treated the imaginary part correctly:

-0.331842471004085e-3 -0.331842471004085e-3*I and

-0.0663684942008172 - 0.0663684942008172*I

Look at plot([0*h[2](x), h[1](x)], x = 0 .. 6, y = -.1 .. .1)

PS: to find possible rounding errors do not use interface(displayprecision = 5), only if you are free of bugs

For Windows you may use its Indexer.

(p+1)*(p-1) = p^2 - 1 is zero modulo 3 by "Little Fermat" (except p=3). Hence one factor divides by 3 and being even (3<=p) it divides by 6.

I once filed Luc Devroye, Non-Uniform Random Variates (1986), having "recipes". May be you can find it as well or find a backup for his site through wayback machine

Likewise you may try x = 1+xi, y=x + eta, z=y+zeta (see attached file, it is Maple 2017, I do not have Maple 2021)

I guess you mean "how to prove it", here a suggestion

Task:=Int(diff(u(x, y), x)*diff(u(x, y), x, y) +
  diff(u(x, y), x, x)*diff(u(x, y), y), x);
A,B:=op(1,%), op(2, %);

X:=IntegrationTools:-Parts(A, diff(u(x,y),x));
Y:=IntegrationTools:-Parts(B, diff(u(x,y),y));

Task=X+Y; combine(%);
lhs(%) - rhs(%);

From that it follows obviously.

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