数列极限的证明如何证明lim((n+2)/(n^2-2))sinn=0

Question

数列极限的证明
如何证明lim((n+2)/(n^2-2))sin n=0

Answer 1

lim(n+2)/(n^2-2)=lim(1/n+2/n^2)/(1-2/n^2)=0.
又|((n+2)/(n^2-2))sin n|