Sign in to follow this  
erlang

P6 IMC 2017

Recommended Posts

Diberikan $f:[0,+\infty)\to \mathbb{R}$ fungsi kontinu sehingga $lim_{x\to +\infty} f(x)=L$ eksis (bisa hingga atau tak-hingga). Buktikan kalau $\lim_{n\to\infty}\int_0^1 f(nx)dx=L$

Share this post


Link to post
Share on other sites
Spoiler

Jika L hingga, untuk setiap $1>\epsilon_1,\epsilon_2>0$, kita bisa pilih $n$ cukup besar sehingga $|f(nt)-L|<\epsilon_1$ untuk $t>\epsilon_2$. Terus ambil limit $\epsilon_1,\epsilon_2$ ke 0 buat tunjukkin riemann sumnya menuju $L$. Buat $L$ hingga mirip

 

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this