Monotone conitnuous function - find limits

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  • #1
daniel_i_l
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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]


Homework Equations





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

  • #2
Dick
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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.
 
  • #3
daniel_i_l
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Thanks.
 

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