Understanding the Problem

The expression ##x^x## is not defined at ##x = 0##. However, we are considering the limit as ##x## approaches 0 from the right (##0^+##). This indicates we're interested in the behavior of the function as ##x## gets very close to 0 but remains positive.

To evaluate this limit, we first take the natural logarithm of both sides to simplify the expression:

Applying L'Hôpital's Rule

Differentiating the numerator and denominator with respect to ##x##, we get:

To find ##L##, we exponentiate both sides:

EXPONENTIAL DISTRIBUTION
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