- 25

- 0

## Main Question or Discussion Point

Hello, it's me again ;)

Problem:

-------

Define

[tex] f_{n}(x)=n^{\alpha}, |x|\leq 1/n, f_{n}=0[/tex] elsewhere

Give all [tex]\alpha \in \Re [/tex] for which

[tex] \lim_{n \to \infty} \int_{\Re}f_{n}(x)dx=+\infty [/tex]

-------

Can i change this last integral to:

[tex] \lim_{x \to 0} \int_{0}^{\infty} x^{-\alpha}dx=+\infty [/tex]

But i think the integration limits aren't correct, and therefore [tex] alpha [/tex] is wrong too.

Any help appreciated,

kind regards,

W.

Problem:

-------

Define

[tex] f_{n}(x)=n^{\alpha}, |x|\leq 1/n, f_{n}=0[/tex] elsewhere

Give all [tex]\alpha \in \Re [/tex] for which

[tex] \lim_{n \to \infty} \int_{\Re}f_{n}(x)dx=+\infty [/tex]

-------

Can i change this last integral to:

[tex] \lim_{x \to 0} \int_{0}^{\infty} x^{-\alpha}dx=+\infty [/tex]

But i think the integration limits aren't correct, and therefore [tex] alpha [/tex] is wrong too.

Any help appreciated,

kind regards,

W.