Wikipedia states that if $f,g$ are real analytic near $c$, and $f,g \to 0$ as $t \to c$, then along any path for which $f>0$ one has $f(t)^{g(t)} \to 1$. The proof Wikipedia cites is in German so I am not able to follow it. How does one show this?
2026-03-30 23:13:17.1774912397
$\lim f(t)^{g(t)} = 0^0 = 1$ if $f,g$ are analytic?
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