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Problem Evaluating a Limit

GROUPS:
Hi All...

I've got a problem when evaluating a limit:

Limit[(a x^r + b y^r)^(1/r), r -> -\]

Machine doesn't work or I (a newbie) am doing something wrong. I'll appreciate a lot any suggestion about how to deal with this.

Thanks in advance.
Answer
11 months ago
There seems to be some issues with the code you have posted. Please try putting it in a Mathematica code section. To do this, paste the code into the editor, highlight it, and then click the Mathematica red spiky logo in the editor.

What are you taking the limit to? What messages or behavior do you see when evaluating this?

If Mathematica only repeats back the input you gave it, then that means that Limit was not able to find a value for the limit you mentioned. Perhaps to solve the problem, certain assumptions have to be made about the values of a, b, x, and y? If so you can use the Assumptions option for Limit. See examples in the documentation for how to use this optional argument to Limit.

For example, Mathematica will not be able to find a value for Limit[(b y^r)^(1/r), r -> Infinity], but if you let it know that y is greater than 0, it will be able to find a result:
Limit[(b y^r)^(1/r), r -> \[Infinity], Assumptions -> {0 < y}]
POSTED BY: Sean Clarke
Answer
11 months ago
Hi,

The main reason why Limit was not able to evaluate the expression is that the relative magnitude of x and y is not known. You need to transform the expression to a simpler form like
x Limit[(1 + b/a (y/x)^r)^(1/r), r -> \[Infinity], Assumptions -> Abs[y/x] <= 1]
where a>0, x>0 and it is assumed that Abs[y/x] <= 1. Similarly for the case Abs[y/x] >= 1. In the above case, Limit[..] will return 1 and the result is x.

Youngjoo Chung
POSTED BY: Youngjoo Chung
Answer
11 months ago