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. 3. Use the definition to show that 4n – 5 lim n00 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 20+ sin Show that the function f(x) = ° is uniformly continuous n00 6. (10, 20] but not uniformly continuous on [10, +o0). on Define a sequence {xn} by x1 2 and an+1 1, 2, 3, .. Show that {n} is convergent and find its limit. (2an +7)/4 7. for n = 8. Show that cos a- - cos y| < |æ – y| for all a and y.
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. 3. Use the definition to show that 4n – 5 lim n00 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 20+ sin Show that the function f(x) = ° is uniformly continuous n00 6. (10, 20] but not uniformly continuous on [10, +o0). on Define a sequence {xn} by x1 2 and an+1 1, 2, 3, .. Show that {n} is convergent and find its limit. (2an +7)/4 7. for n = 8. Show that cos a- - cos y| < |æ – y| for all a and y.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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