## Maple / a logical question

My lecturer gave us the following question:

$f(x):=\frac{x}{x^{sin(x)}-1}$

Using Maple, find the limit of f(x) in $x=0^+$.
In order to approve Maple's answer, find the answers of the following equations:
* $f(x)=-0.1$ ( I got something with $10^-4$)
* $f(x)=-0.01$ ( I got something with $10^-44$)
* $f(x)=-0.001$ ( I got something with $10^-435$ )

According to your answers, how many digits should maple work with in order to find the solution of:
$f(x)=-10^{-10}$
?

Now, I think I got the idea, I just want you to approve / support it: I believe that if you create a series out of the answers, you get:
$a_1=-4, a_2=-44, a_3=-435, ...$
Therefore, a_10 should be something like $435 * 10^{-7}$.

Is my 'logic' right?