\(\displaystyle n \in \mathbb{N}\), \(\displaystyle sin(1/x)/x^n \to 0\), as \(\displaystyle x\to \infty\). Only thing I know is \(\displaystyle sin(1/x)/x^n\leq1/x^n\). How should I even begin to start to prove this statement?
I think I got it now but I am not sure if this can be done. Can we simply say since \(\displaystyle sin(1/x) \cdot 1/x^n\) and since \(\displaystyle sin(1/x) \to 0\) and \(\displaystyle 1/x^n \to 0\) as \(\displaystyle x \to \infty\) implies that \(\displaystyle sin(1/x)/x^n \to 0\) as \(\displaystyle x \to \infty\). Can I do this in this problem?
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.