Question

lim(3sinn-4cosn+5)/(2n^5+1) giúp mình vs chuẩn bị mình đi hc rr plss

 

Answer 1

Do \(\left\{{}\begin{matrix}-1\le sinn\le1\\-1\le cosn\le1\end{matrix}\right.\)

\(\Rightarrow-2\le3sinn-4cosn+5\le12\)

\(\Rightarrow\dfrac{-2}{2n^5+1}\le\dfrac{3sinn-4cosn+5}{2n^5+1}\le\dfrac{12}{2n^5+1}\)

Mà \(lim\dfrac{-2}{2n^5+1}=\lim\dfrac{12}{2n^5+1}=0\)

\(\Rightarrow\lim\dfrac{3sinn-4cosn+5}{2n^5+1}=0\)