• Support PF! Buy your school textbooks, materials and every day products Here!

Monotone conitnuous function - find limits

  • Thread starter daniel_i_l
  • Start date
daniel_i_l
Gold Member
867
0
1. Homework Statement
if f is monotonic and continues in R, and [tex]\int^{\infty}_{a} f(x)dx[/tex] converges then
[tex]lim_{x \rightarrow \infty} xf(x) = 0 [/tex]


2. Homework Equations



3. The Attempt at a Solution
I know that if xf(x) converges at all then it has to convergs to 0. But how do I know that it converges?
Thanks.
 

Answers and Replies

Dick
Science Advisor
Homework Helper
26,258
618
Can you show that for any positive value of k however small, that f(x)<k/x for all x>N for N sufficiently large? Hint: suppose it's not.
 
daniel_i_l
Gold Member
867
0
Thanks.
 

Related Threads for: Monotone conitnuous function - find limits

Replies
3
Views
658
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
2
Views
934
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
2
Views
687
  • Last Post
Replies
1
Views
1K
Top