$\large \lim_{x\to 0^+} x = 0 \qquad \qquad \lim_{x\to0^+} x^x = 1$

The two limits above are commonly used in calculus textbooks. However, the following limit isn't! What is the value of this limit?

$\large \lim_{x\to0^+} x^{x^x}$

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