- #1
Zaphodx57x
- 31
- 0
I'm not sure how to solve these problems. The example given in the book does not use trig functions. Any insight into how I solve these would be helpful.
Find the following rates of convergence.
[tex]
\lim_{n\rightarrow infinity} sin(1/n) = 0
[/tex]
My thought would be to do the following
[tex]
|sin(1/n) - 0| <= 1
[/tex]
But the book says to get a rate in the form [tex]1/n^p[/tex]
The following also gives me trouble.
[tex]
\lim_{n\rightarrow infinity} sin(1/n^2) = 0
[/tex]
which seems like it should converge faster than the the first one.
Find the following rates of convergence.
[tex]
\lim_{n\rightarrow infinity} sin(1/n) = 0
[/tex]
My thought would be to do the following
[tex]
|sin(1/n) - 0| <= 1
[/tex]
But the book says to get a rate in the form [tex]1/n^p[/tex]
The following also gives me trouble.
[tex]
\lim_{n\rightarrow infinity} sin(1/n^2) = 0
[/tex]
which seems like it should converge faster than the the first one.