What is the best method to solve the limit $\lim_{x\to \infty}\biggl(1+\sin\frac{2}{x^2}\biggr)^{x^2}$? By the looks of it, I would say the following is a Neperian limit: $$\lim_{x\to \infty}\biggl(1+\sin\frac{2}{x^2}\biggr)^{x^2}$$
but I could not find a way to algebraically bring it in the form: $$\lim_{x\to \infty}\biggl(1+\frac{k}{x}\biggr)^{mx} = e^{mk}$$
Any suggestion on how to solve this?

You can use this:
If $a \to 1$ and $b \to \infty$, then $\lim a^b = \exp(\lim (a-1)b)$
