Math 455                       Homework                      Saff&Snider
Sec 5.3
___________________________________________________________________________

#6b.  By its definition, f is differential for all z not equal to zero.
      So, there is only the question of differentiability at z=0.

      f'(0) = lim_{z->0} {(f(z)-f(0))/(z-0)}

	    = lim_{z->0} {(1/z) (sin z / z - 1)}

	    = lim_{z->0} {(sin z - z) / z^2}

	    = lim_{z->0} {(cos z - 1) / 2z}

	    = lim_{z->0} {-sin z / 2}

	    = 0

      using the Lahopital's rule repeatedly.  Hence, f'(0) exists and
      f is analytic there.
_____________________________________________________________________________