1. Find the Taylor or Laurent series, whichever appropriate, of a) f(z) = e²-/(z - 2)² about z = 2, b) f(z) = z/(z² + 1) about z = 0 for |z| > 1. In each case, write explicitly at least the first three terms of the series. [You may find it useful to recall that the Maclaurin series of e? is E-o z"/n!.] Zn=0

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For a Taylor series to exist and give the exact value of f (x), which of the following must be true?   a. The function f (x) must be differentiable an infinite number of times. b. Taylor series must converge. c, The function f (x) must be differentiable an infinite number of times, and the Taylor series must converge.