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How to find the limit limit(u(x,t),t=infinity), where u(x,t) is the solution of the Cauchy problem:
pde:=diff(u(x,t),t)=diff(u(x,t),x,x)+exp(-t) with the initial condition
ic:=u(x,0)=arctan(x) ?

E := proc (phi) options operator, arrow; int(1/(1-(1-1/kappa^2)*sin(phi)^2)^(1/2), phi = 0 .. phi) end proc

E(pi/2)

Is there a way to get this function to work properly without having to simplify the integral manually ?

kappa is a constant (with a value of 12.4)

Thanks in advance!

Hi,

I just noticed something rather peculiar (well, to me, at least). When I compute the limit

limit((1-1/x)^(-x),x=-infinity)

as is, I get the expected result of exp(1).

However, if I load the RealDomain package prior to computing the limit,

with(RealDomain):

limit((1-1/x)^(-x),x=-infinity)

I get that the limit is undefined. 

Any ideas as to why that is the case? Thanks!

Does anybody have such package that converts function in series of powseries package i.e. addable, substructuble and so on. And mayby with functionality of series itself i.e. remember asymptotic point for which O(x^n) was present as simple series returns. I think with such pakage limit in attach limit_test.mw

Besides of other things i should also analyze what happens with function at y=0. For now IntermediateCalc incapsulates limit but it too slow. What can you suggest better? Tried series but there is the problem that function is only defined at right of 0, there is no expansion in this case. See attach for deatails. main.mw

How to find the limit

>limit(sum(1/binomial(n, k), k = 1 .. n),n=infinity);

with Maple?

How to find the limit
limit(sum(n*x/(n^2+x)^2, n = 1 .. infinity), x = infinity);
with Maple?

I have been running up against a memory limitation when running maple.java v15 from a Linux Ubuntu workstation.  The memory indicator in Maple gets up to 39.36M but will not go above that.  After I reach this limit I am still able to perform further computations but Maple gets slow and eventually crashes.  Here is one of the lines from the error message:

Exception in thread "AWT-EventQueue-0" java.lang.OutOfMemoryError: GC overhead limit exceeded

Hi

When the numerator of a quotient is a negative integer, Maple puts the quotient into parentheses and the negative sign before the quotient (not with the numerator). Here is an example:

with(RandomTools);
a1 := Generate(integer(range = -10 .. -1));
Limit(a1/(x-3), x = 3, right);

I would like to have the negative sign with the numerator and to remove the parentheses.

I tried to export the limit in MathML, but it didn't work.

In...

Hello all,

 Is any anyone know how good is maple numeric stiff ode solver (stiff=true) ? What i mean is how many stiff ode's it can handle at a given time. I am having a hardtime solving a system of ode's (say 300 stiff ode's). Is there any other numeric stiff ode solver in maple that can handle large number of ode's?

I used islode advanced numeric solver for stiff ode's and it also has some limitations on the number of ode's and moreover it is slow.

I have Maple 15. I am trying to calculate the limit of this function

((x^3-2x^2+sin(x))^(1/3))/(6x+2)

for x tend to +infinity. As you can get it with a rapid manual calculus, this limit is 1/6. But Maple returns undefined for this very simple limit. Why? How can i get Maple to calculate limits correctly? Derive 6 return the correct answer 

Is there an easy way to find the limit of the following equations as Pec_i approches infinity.

 Equation 1

(Q*(R*S+1-S)/(1-R*R3*k*(1-R1)/C/Pec_i*S)*(H_vap+1/(1-exp(Pec_i)))*exp(C*Pec_i/(R*S+1-S)*(1-R*R3*k*(1-R1)/C/Pec_i*S)*S/k)-H_vap)*(1-exp(Pec_i*(1-S)/(R*S+1-S)*(1-R*R3*k*(1-R1)/C/Pec_i*S))) = 1;

 Equation 2

 Theta0/C = (exp(Pec_i/(R*S+1-S)*(1-R*R3*k*(1-R1)/C/Pec_i*S)*(1-S))-1)*(H_liq+1/(1-exp(-C/k*Pec_i/(R*S+1-S)*(1-R*R3*k*(1-R1)/C/Pec_i*S)*S)));

I have a maple exercise where it ask me to find the limit of a sum, here what's I type

f:= 2*k/(2*k+11);

g:= sum(f,k=1..n);

limit(n^(11/2)*g,n=infinity);

It spit out the answer infinity

but the answer is 10395/64*Pi^(1/2), can anyone tell me what am i doing wrong

Hey guys. Can you help me with this problem? I'm trying to plug in a snowflake equation in finding the perimeter of a snowflake on the nth step. The function is as follows:

p:=n->(3*(3/4)^k, k=1..n);
                                   

I'm trying to find the limit of this equation and it's suppose to give me infinity by using this command:

limit(pn(n), n=infinity);     but it's not quite giving me the limit. The limit is...

How to find the limit
limit(int(abs(sin(f(x))), x = 0 .. T)/T, T = infinity) assuming T::positive;
with Maple in the cases: a) f:=x->x^2; b) f:=x->x*exp(x)?

PS. Or to establish its nonexistence.