Mathematica - compute limit

Author

compute limit

Frank Hechtner

2006-10-19, 4:21 am

Hi,

i?m in trouble with the calculation of limits. my expression is the
following

((1 + r)^t*(1 - s) + s)^(1/t) - 1, t -> ?

as you see, the limit is r when x approaches ?.

Unfortunately when using limit the output is

Limit[((1 + r)^t*(1 - s) + s)^(1/t) - 1, t -> ?].

I dont see whats going wrong. Does limit only compute numerical expression?

Thanks for your help

Frank

ben

2006-10-20, 4:18 am

Dear Frank,

you have to tell Mathematica sth about your
variables, i.e. which is real, positive, ...;
otherwise Mathematica assumes them to be complex.
But for arbitrary complex numbers a closed solution
need not exist.

Try this

Limit[((1 + r)^t*(1 - s) + s)^(1/t) - 1, t -> \[Infinity],
Assumptions -> {r > 0, s > 0, s < 1}]

Bye
Ben

Frank Hechtner schrieb:

> Hi,
>
> i?m in trouble with the calculation of limits. my expression is the
> following
>
> ((1 + r)^t*(1 - s) + s)^(1/t) - 1, t -> ?
>
> as you see, the limit is r when x approaches ?.
>
> Unfortunately when using limit the output is
>
> Limit[((1 + r)^t*(1 - s) + s)^(1/t) - 1, t -> ?].
>
> I dont see whats going wrong. Does limit only compute numerical expression?
>
> Thanks for your help
>
> Frank

Scout

2006-10-20, 4:18 am

Hi Frank,
in your expression there are symbols not defined.
I'll try to define them in this attempt:

In[1]:=Assuming[{r>0,0<s<1},
Limit[((1 + r)^t*(1 - s) + s)^(1/t) - 1, t ->Infinity]]

Out[1]= r

HTH,
~Scout~

"Frank Hechtner" <frank.hechtner@rub.de>
news:eh79cr$dpb$1@smc.vnet.net...
> Hi,
>
> i?m in trouble with the calculation of limits. my expression is the
> following
>
> ((1 + r)^t*(1 - s) + s)^(1/t) - 1, t -> ?
>
> as you see, the limit is r when x approaches ?.
>
> Unfortunately when using limit the output is
>
> Limit[((1 + r)^t*(1 - s) + s)^(1/t) - 1, t -> ?].
>
> I dont see whats going wrong. Does limit only compute numerical
> expression?
>
> Thanks for your help
>
> Frank
>

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