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#344 Tube Plots ←	↑	→ #346 Returns formal integration sign for (1 + tan(x))^(1/3), which is elementary

#345 fails to compute some simple limits

Edit detail for #345 fails to compute some simple limits revision 4 of 5

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Editor: test1 Time: 2014/04/15 18:06:25 GMT+0
Note:

changed:
-... how can I calculate the limit of:
- 
-$$(3^x+5^x)^{1/x}$$
- 
-for $x \rightarrow +\infty$?
... how can I calculate the limit:
 
$$\lim_{x \rightarrow +\infty}(3^x+5^x)^{1/x}$$

On March 25, 2007 11:54 AM Ondrej Certik asked:

... how can I calculate the limit:

$\lim_{x \rightarrow +\infty}(3^x+5^x)^{1/x}$

The result is 5 as you can check by hand:

$(3^x+5^x)^{1/x} = 5 <em> ((3/5)^x+1)^{1/x} \rightarrow 5$

When I tried that in axiom:

fricas

limit((3^x+5^x)^(1/x), x=%plusInfinity)

$\label{eq1}5$

(1)

Type: Union(OrderedCompletion?(Expression(Integer)),...)

or the equivalent problem:

fricas

limit((3^(1/x)+5^(1/x))^(x), x=0, "right")

$\label{eq2}5$

(2)

Type: Union(OrderedCompletion?(Expression(Integer)),...)

I got "failed".

Now it works.

... --kratt6, Thu, 20 Dec 2007 02:11:48 -0800 reply

Category: Axiom Mathematics => Axiom Library