527ass1 - will need to use the trick of Example 4(b I have...

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642:527 ASSIGNMENT 1 FALL 2009 Turn in starred problems Thursday 09/10/2009. Multiple-page homework must be STAPLED when handed in. Section 4.2: 1 (a), (d), *(e), (g), *(k) 2 (b), (d), *(e) *6 3 (a), (e), (i), *(m) 7 (a), *(f), (i), (j) Hints and remarks: (a) For the problems of 4.2.1 I ±nd it convenient to use the ratio or root test directly to determine for what values of x the series converges, rather than use the formulas (7a) or (7b). These work but some care is needed; for some problems you
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Unformatted text preview: will need to use the trick of Example 4. (b) I have listed problem 4.2.6 before problem 4.2.3 because 4.2.6 teaches us an important lesson about ±nding Taylor series: it is frequently easiest to get a Taylor series starting from some other Taylor series that one knows, rather than using formula (16) on page 181. For example, in 3(a) it helps to write e x = e e x-1 . For 3(m) one should start from formula (6.2), page 192....
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This note was uploaded on 12/15/2009 for the course MATH 527 taught by Professor Staff during the Fall '08 term at Rutgers.

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