daniel_i_l

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**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.