- #1

Nathanael

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## Homework Statement

I want to integrate [itex]\int_0^e \ln(x)[/itex] but first, I wondered if it would be divergent. I figured if x

^{x}goes to zero as x goes to zero then the integral would diverge (because xln(x)-x would diverge).

**2. The attempt at a solution**

I'm wondering how you could show that this limit (x

^{x}as x→0) is 1. It makes intuitive sense that it should approach 1, and it's clear from the graph, but I'm curious as to how someone would find this limit mathematically.