Z.B. mit L'Hospital:
\(\color{white}{=}\lim\limits_{x\to 0}x^{-x} \\
= \lim\limits_{x\to 0}\exp\left(-x\ln(x)\right) \\
=\exp\left( \lim\limits_{x\to 0}-x\ln(x)\right) \\
=\exp\left( -\lim\limits_{x\to 0}x\ln(x)\right)\\
=\exp\left( -\lim\limits_{x\to 0}\dfrac{\ln(x)}{1/x}\right) \\
=\exp\left( -\lim\limits_{x\to 0}\dfrac{[\ln(x)]'}{[1/x]'}\right)\\
=\exp\left( -\lim\limits_{x\to 0}-x\right)\\
=\exp \left(0\right)\\
=1\)
Sonstiger Berufsstatus, Punkte: 16.5K
─ SrenWierzba 11.09.2019 um 00:37