This evening I thought of the following question that isn't related to homework, but it's a question that seems very challenging to me, and I take some interest in it.
Let's consider the following function: $ f(x)= \left(\frac{\sin x}{x}\right)^\frac{x}{\sin x}$ I wonder what is the first derivative (1st, 2nd, 3rd ...) such that $\lim\limits_{x\to0} f^{(n)}(x)$ is different from $0$ or $+\infty$, $-\infty$, where $f^{(n)}(x)$ is the nth derivative of $f(x)$ (if such a case is possible). I tried to use W|A, but it simply fails to work out such limits. Maybe i need the W|A Pro version.