A towering limit
Calculus
Level
3
\[ \Large \lim_{n\to\infty} \left( n \sin \dfrac \pi n\right)^{\left( 1 + \frac \pi n\right)^n} \]
The limit above has a closed form. Find the value of this closed form.
If this limit can be approximated as \(3.19\times 10^\eta\), where \(\eta \) is an integer, find \(\eta\).
You may use a calculator for the final step of your calculation.
by
Rohith M.Athreya