$$\lim_{n \to \infty}\left(\frac{\log{\left(\frac{1}{n^{\frac{2}{5}} \sin{\left(\frac{1}{n^{\frac{2}{5}}} \right)}} \right)}}{n^{2}}\right) = 0$$
$$\lim_{n \to 0^-}\left(\frac{\log{\left(\frac{1}{n^{\frac{2}{5}} \sin{\left(\frac{1}{n^{\frac{2}{5}}} \right)}} \right)}}{n^{2}}\right)$$
Más detalles con n→0 a la izquierda$$\lim_{n \to 0^+}\left(\frac{\log{\left(\frac{1}{n^{\frac{2}{5}} \sin{\left(\frac{1}{n^{\frac{2}{5}}} \right)}} \right)}}{n^{2}}\right)$$
Más detalles con n→0 a la derecha$$\lim_{n \to 1^-}\left(\frac{\log{\left(\frac{1}{n^{\frac{2}{5}} \sin{\left(\frac{1}{n^{\frac{2}{5}}} \right)}} \right)}}{n^{2}}\right) = - \log{\left(\sin{\left(1 \right)} \right)}$$
Más detalles con n→1 a la izquierda$$\lim_{n \to 1^+}\left(\frac{\log{\left(\frac{1}{n^{\frac{2}{5}} \sin{\left(\frac{1}{n^{\frac{2}{5}}} \right)}} \right)}}{n^{2}}\right) = - \log{\left(\sin{\left(1 \right)} \right)}$$
Más detalles con n→1 a la derecha$$\lim_{n \to -\infty}\left(\frac{\log{\left(\frac{1}{n^{\frac{2}{5}} \sin{\left(\frac{1}{n^{\frac{2}{5}}} \right)}} \right)}}{n^{2}}\right) = 0$$
Más detalles con n→-oo