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Download e-book for iPad: A First Course in Real Analysis by M. H. Protter C. B. Morrey Jr.

By M. H. Protter C. B. Morrey Jr.

ISBN-10: 1461599903

ISBN-13: 9781461599906

ISBN-10: 146159992X

ISBN-13: 9781461599920

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Additional resources for A First Course in Real Analysis

Sample text

A2 ) 6. lim x--+l+(x":" 1)/~ 8. limx_>+ ",(x 2 + 1)/ x 3 / 2 10. limx--++ ",(Y x 2 + 2x - x) 11. 14. 12. 15. 13. 15 with x~ - 00 instead of 14. , x~a+ instead of x~a). 15. 17. 16. 17(a). 17. Suppose f(x)~ + 00 and g(x)~ - 00 as x~ f and g with these properties and such that + 00. Find examples of functions (a) limx--++ ",[f(x) + g(x)] = + 00 (b) limx.... + ",[f(x) + g(x)] = - 00 (c) limx--++",[f(x) + g(x)] = A, A an arbitrary real number 18. Find the values of p, if any, for which the following limits exist.

15. Prove by induction that (XI k + X2 + ... + 2(XIX2 + XIX) + ... + XIXk 29 I: The real number system 16. 24. 17. 25. 18. 26. 19. 27. ] 20. 28. ] 21. 29. 22. 2. 23. 2. 24. 2. 5 We denote by N x N the set of all ordered pairs of natural numbers (m, n). State and prove a Principle of mathematical induction for sets contained in NXN. 5 An asterisk is used to indicate difficult problems. 1 Continuity Most of the functions we study in elementary calculus are described by simple formulas. These functions almost always possess derivatives and, in fact, a portion of any first course in calculus is devoted to the development of routine methods for computing derivatives.

20. 28. ] 21. 29. 22. 2. 23. 2. 24. 2. 5 We denote by N x N the set of all ordered pairs of natural numbers (m, n). State and prove a Principle of mathematical induction for sets contained in NXN. 5 An asterisk is used to indicate difficult problems. 1 Continuity Most of the functions we study in elementary calculus are described by simple formulas. These functions almost always possess derivatives and, in fact, a portion of any first course in calculus is devoted to the development of routine methods for computing derivatives.

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A First Course in Real Analysis by M. H. Protter C. B. Morrey Jr.


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