4. (a) 10glO x = I:~=l (_1)k+ 1(x _l)k /(k log 10), valid for x E (0,2]....
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4.
(a) 10glO x = I:~=l (_1)k+ 1(x _l)k /(k log 10), valid for x E (0,2].
(b) x2 + 2x-
1 = 2 + 4(x - 1) + (x - 1)2, valid for x E R.
(c) eX = I:~o e(x - l)k /k!, valid for x E R.
10. See Exercise 4 in Section 5.1 and use analytic continuation.
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