91Ó°ÊÓ

Prove that the limit \(\lim _{n \rightarrow+\infty}\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}\right)-\log n\) exists. The constant $$ r=\lim _{n \rightarrow+\infty}\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}\right)-\log n $$ is called the Euler-Mascheroni constant. It is not known whether \(\gamma\) is irrational.

Find the 100 - th derivative of \(x \rightarrow x^{2} \sin x\).