## limit sup inf of function...

Hi

I would like to compute the limit as t goes to infinity.

Let delta be a given positive real number

restart;
assume(t, positive);

g := (t,delta) arrow  maximization(minimization(abs(x^(2^(-t))-y), y = 0 .. delta), x = 0 .. 1) ;

then I would like to compute the limit of g(t,delta) as t goes to infinity

Many thanks for any help

## Minimize function using maple ...

Hi

I would like to compute the limit as t goes to +infinity of

restart;
assume(t, positive);

g(t):=minimize(abs(x^(2^(-t))-1),x=1-delta.1+delta);

where delta is very small such that 1- delta is positive.

Then I would like to compute the limit as to goes to infinity of g(t)

Many thanks

## Bug in limit

Maple 2016

Let us consider

restart;
MultiSeries:-limit(sin(n)/n, n = infinity, complex);
0

The answer is wrong: in view of the Casorati-Weierstrass theorem the limit does not exist. Let us try another limit command of Maple

limit(sin(n)/n, n = infinity, complex);

(lim) (sin(n))/(n)

which fails. Therefore, Maple user does not obtain the correct answer.

## is it possible to trace limit() steps? Which Maple...

Any one know if it possible to see the steps used by the limit() function as one does with many other functions such as dsolve and int ?  This is what I tried

restart;
infolevel[limit]:=5;
interface(verboseproc=3);
limit(x^2 *log(x),x=0);

But I see no steps, only the final answer. Are not all Maple functions possible to trace? How does one know which functions can generate trace and which do not?

I am using Maple 2016.1

I wanted to see something like:

let x=1/t, hence expression becomes  (-ln t)/t^2, now taking limit as t->infinity. Applying L'Hopital rule, limit t->infinity of -1/(2 t^2) which gives zero.

I assumed this is something what Maple does internally, (but there are other ways also) and wanted to see what Maple does.

## Incompetent results of Student[Precalculus]:-Limit...

Maple 2016

Let us consider

Student[Precalculus]:-LimitTutor(sqrt(x), x = 2);

One expects a nice illustration of the result sqrt(2). But instead of that one reads "f(x) approaches 1.41 as x approaches 2". This is simply ignorant and forms a wrong understanding of limits. It should also be noticed that all the entries (left, 2-sided, and right) produce the same animation. The same issue with other limits I tried, e.g.

Student[Precalculus]:-LimitTutor(sqrt(x), x = 1);

. I think this command should be completely rewritten or excluded from Maple.

## Weakness in limit and MultiSeries:-limit

Maple

Let us consider

J := int(x^n/sqrt(1+x^n), x = 0 .. 1) assuming n > 0;

2*(2^(1/2)-hypergeom([1/2, 1/n], [(n+1)/n], -1))/(2+n)

limit(J,n=infinity);
FAIL
MultiSeries:-limit(J,n=infinity);
FAIL

Mma 11 finds the limit is zero. Hope one feels the difference.

## Discordance of outputs of two limit commands

Maple
limit((x^2-1)*sin(1/(x-1)), x = infinity, complex);
infinity-infinity*I
MultiSeries:-limit((x^2-1)*sin(1/(x-1)), x = infinity, complex);
infinity

whereas the same outputs are expected. The help http://www.maplesoft.com/support/help/Maple/view.aspx?path=infinity&term=infinity does not shed light on the problem. Here are few pearls:

• infinity is used to denote a mathematical infinity, and hence it is usually used as a symbol by itself or as -infinity.
• The quantities infinity, -infinity, infinity*I, -infinity*I, infinity + y*I, -infinity + y*I, x + infinity*I and x - infinity*I, where x and y are finite, are all considered to be distinct in Maple. However, all 2-component complex numerics in which both components are infinity are considered to be the same (representing the single point at the "north pole" of the Riemann sphere).
• The type cx_infinity can be used to recognize this "north pole" infinity.

## Error, (in Engine:-Dispatch) not implemented yet: ...

sorry what is what dispatch and implementing what? i get these every week for a number of cases sometimes it specifies that it is an "unhandled psi case" still waiting on that built in proc u guys where gonna dispatch like u know the reasons ppl always have a whinge about evalf not working in some cases  anyway a few people have run into these error id say.

## query "undefined" specifics...

when a term in the evaluation of some calculus functions particularly, i sometimes arrive at output in the general form as follows:

Algebraic expression + undefined

i am just wondering if there is a function i can call that will return the specific details as to what error the term "undefined" placeholder has stored im assuming such information is held, ie is it undefined as a consequence of the limits either side not being equal to one another or is it a 0/0 evaluation.

## distributing limit to each terms...

Hello people in mapleprimes,

I want to distribute limit or Limit to each terms of summation.

Limit(f(a+h)-f(a),h=0);

But, the output is not distributed one, but the same as the input, though

I want it to become Limit(f(a+h),h=0)+Limit(f(a),h=0), or

Limit(f(a+h),h=0)+f(a).

Isn't there any way for it, other than a trivial one that is

subs(Limit(f(a+h)-f(a),h=0)=Limit(f(a+h),h=0)+Limit(f(a),h=0),Limit(f(a+h)-f(a),h=0));

?

I hope someone will teach me.

taro

## limit of multivariate function...

Hello people in mapleprimes,

I have a question. I hope someone give an answer to me.

rho:=sqrt((x-a)^2+(y-b)^2);

limit(x-a+y-2,rho=0);

brings an error

Error, invalid input: limit expects its 2nd argument, p, to be of type Or(name = algebraic, set(name = algebraic)), but received ((x-a)^2+(y-b)^2)^(1/2) = 0

Isn't other way than the following?

limit(x-a+y-2,{x=a,y=b});

Best wishes.

taro

## Lyapunov exponent...

How I can solve this:

for different fn(x0) ? for f(x)=exp(x^2(a-x))

## Does the principal value of this integral exist?...

I want to make sense of the expression

Int(t^2/ln(t)*exp(-t), t=0..infinity);

The denominator vanishes at t=1.  The singularity at t=1 is not integrable.  I want to see whether the integral is defined in the sense of Cauchy principal value.  Thus, I let

K := Int(t^2/ln(t)*exp(-t), t=0..1-a) + Int(t^2/ln(t)*exp(-t), t=1+a..infinity);

and wish to see whether the following limit exists:

limit(K, a=0, right);

Maple cannot evaluate this.  Nor can I.  Alternatively, we may try:

series(K, a=0);

or

series(K, a=0) assuming a>0, a<1;

In both cases Maple says that it is unable to compute the series.

So my question is: Does the Cauchy principal value exist, and can Maple help one to determine that?

## What is that limit?...

The following integral
f := u-> int(-1/(x*sqrt(-1+u^2*(x+1)^2*x^2)), x = (1/2)*(-u-sqrt(u^2-4*u))/u .. (1/2)*(-u+sqrt(u^2-4*u))/u);
plot on RealRange(4,infinity), limit(f(u),u=4,right), limit(f(u),u=infinity).
Unfortunately, I lost a file. As far as I remember it, I have had a problem with
the last-named one only:

limit(f(u), u = infinity);

MultiSeries:-limit(f(u), u = infinity);

asympt(f(u), u, 2);

Error, (in asympt) unable to compute series

Hope my colleagues will make progress with it. The assumed value is Pi/2.

## Problem with procedure including limit...

how to make below can be successfully run?

normaldiff := proc(f1)
return limit((subs(x=x+h,f1)-f1)/h, h=0):
end if:
recurdiff := proc(f2)
if f2 = 0 then
return 0:
end if:
if f2 <> 0 then
return limit((subs(x=x+h,normaldiff(f2)+recurdiff(f2))-(normaldiff(f2)+recurdiff(f2)))/h, h=0):
end if:

f := x;
normaldiff(f)+recurdiff(f);

expect return 1, is like normal diff

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