For the first part, as x → 0 from the positive side, ln(x)/√x → -infinity/0 (0 from the + side). This is not indeterminate, so don't try L'Hopital's rule here. Both the numerator and the denominator drive f to -infinity.
For the second part, let y=f(x). For x=-1,
y=ln(-1)/i iy=ln(-1) e^iy=-1
From this arrangement, we see that y=pi (Euler's law).
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