Answer to Question #8072 in Real Analysis for Mike

Question #8072

Show that f=O(1) [this is the letter O not the number 0] as x->a if and only if f(x) is bounded on some neighborhood of a.

Expert's answer

Download Answer

Learn more about our help with Assignments: Real Analysis

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Show that f =o(1) as x->a if and only if f(x)->0 as x->a.
2. The statement "If f = o(g) then f = O(g)" can be abbreviated o⇒O. Prove this.
3. Show that K(x-a) = O(k-a) [this is the letter O no the number 0] for any K.
4. If K is a constant, show that K(x-a) = o(x-a) [yes that is a "o" not a "0"] if a
5. Task If (a sub_n) and (b sub_n) are cauchy sequences, show directly that (a sub_n + b sub_n) is also
6. Let x_sub(1) = a>0 and x_sub(n+1) = x_sub(n) + 1/x_sub(n). Show that x_sub(n) diverges
7. Show that it is possible to have a sequence (x_sub(n)) diverge while the sequence (|x_sub(n)|) conve