Does assigning a large value to a variable do the job of var -- inf well?

In symbolic matlab there is limit(f,x, inf) but in non-symbolic calculation...?

[Stephen23]

Original question posted by Mirlan Karimov, recovered from Google Cache:

Does assigning a large value to a variable do the job of var -- inf well?

In symbolic matlab there is limit(f,x, inf) but in non-symbolic calculation...?

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[John D'Errico]

Be serious. Does it do the job well? Yes. Or definitely not. Probably maybe, approximately so. To answer your question completely would take writing a book about limits, about numerical analysis. I could as easily give an example where the use of any large number is a terrible approximation. Another example where it is great.

Lets see, what is the sum as n--> inf of the terms 1/(n + log(n))? Is the infinite series convergent or divergent? How many terms do you need to convince yourself of the solution?

How about computing the sum as n--> inf of 1/n^2? How large does n need to be?

What is the limit as x --> inf, of erfc(x)? How large does x need to be that the result is close to the true value?

How many terms are needed for convergence of the Taylor series for sin(x) to within some tolerance? If x=0.1? x=5? x=100?

The point is, how large does large need to be is completely problem dependent. Knowing the answer requires understanding the mathematics of what you are doing.