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Show that the function f(x) = is uniformly continuous on [10, 20] but not uniformly continuous on [10, +00). 6.

Show that the function f(x) = is uniformly continuous on [10, 20] but not uniformly continuous on [10, +00). 6.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 32EQ
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Use mathematical induction to show that >(4k – 1) = n(2n + 1) k=1 for all n > 1. 2. . Let U = (0, 1) U (2, 3) U (4, 5) be a union of three open intervals and A= [0, 10] \ U. Show that A is compact. Use the definition to show that 4n – 5 lim n+00 2n + 3 = 2. 4. Use the definition to show that x + x – 6 lim = 5. x - 2 5. Calculate the following limits lim n(vn2 +1-n), lim 0+ sin Show that the function f(x) = a is uniformly continuous n00 6. on [10, 20] but not uniformly continuous on [10, +o0). (2x, +7)/4 Define a sequence {xn} by x1=2 and xn+1= for n = 1, 2, 3, .. Show that {rn} is convergent and find its limit. 7. 8. Show that cos a- cos y < |æ – y| for all a and y. 3.
Transcribed Image Text:Use mathematical induction to show that >(4k – 1) = n(2n + 1) k=1 for all n > 1. 2. . Let U = (0, 1) U (2, 3) U (4, 5) be a union of three open intervals and A= [0, 10] \ U. Show that A is compact. Use the definition to show that 4n – 5 lim n+00 2n + 3 = 2. 4. Use the definition to show that x + x – 6 lim = 5. x - 2 5. Calculate the following limits lim n(vn2 +1-n), lim 0+ sin Show that the function f(x) = a is uniformly continuous n00 6. on [10, 20] but not uniformly continuous on [10, +o0). (2x, +7)/4 Define a sequence {xn} by x1=2 and xn+1= for n = 1, 2, 3, .. Show that {rn} is convergent and find its limit. 7. 8. Show that cos a- cos y < |æ – y| for all a and y. 3.
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