(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]f: [0,+\infty) \to \mathbb{R}: y \mapsto \int_0^{+\infty} y \arctan x \exp(-xy)\,dx.

[/tex]

Show that this function is continuous in [tex]y[/tex] if [tex]y \neq 0[/tex]

and discontinuous if [tex]y = 0[/tex]

2. Relevant equations

3. The attempt at a solution

I just can't get started, any hint?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Where is the following function continuous

**Physics Forums | Science Articles, Homework Help, Discussion**