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

I have to prove that the solution of an ODE can be continued to a function [tex] \in \mathcal{C}^1(\mathbb{R}) [/tex]. The solution is:

[tex]e^{-\frac{1}{x^2}} \int_{x_0}^x -\frac{2e^{\frac{1}{t^2}}}{t^2} dt [/tex]

It is clear that this function is not defined in [tex] x=0 [/tex]. Its limit for [tex]x \rightarrow 0 [/tex] though, seems to be zero. How do I prove it?

2. Relevant equations

Actually prove that the limit is zero.

3. The attempt at a solution

Should I use the dominated convergence theorem? Can't find the right function to dominate this one...

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# Homework Help: Integral estimate.

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