My lecturer gave us the following question:

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

Using Maple, find the limit of f(x) in $\displaystyle x=0^+$.

In order to approve Maple's answer, find the answers of the following equations:

*$\displaystyle f(x)=-0.1$ ( I got something with $\displaystyle 10^-4 $)

*$\displaystyle f(x)=-0.01$ ( I got something with $\displaystyle 10^-44 $)

* $\displaystyle f(x)=-0.001$ ( I got something with $\displaystyle 10^-435$ )

According to your answers, how many digits should maple work with in order to find the solution of:

$\displaystyle f(x)=-10^{-10}$

?

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:

$\displaystyle a_1=-4, a_2=-44, a_3=-435, ...$

Therefore, a_10 should be something like $\displaystyle 435 * 10^{-7}$.

Is my 'logic' right?

Thank you for your time