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?

Thank you for your time