= 5. Prove that if x1 = 1 and rn+1= V6 + xn, then xn <3 for all integers n > 1.e 6. Let E CR such that E is nonempty and bounded. Prove that the set -E ={-x :fies inf(E) = - sup(-E). se 8. If x, y ER with x < y, prove that x < tx + (1 – t)y < y for all t e (0,1).se 9. Prove that if A and B are countable sets, then A x B and AUB are countable.se 10. Is the set of all finite sequences of Os and 1s countable? Justify your answer.

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Answered: = 5. Prove that if x1 = 1 and xn+1 = V6…

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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Choose the correct option. The number of onto function from the set {1,2,….,11} to the set {1,2,….,10} is- (a)5×⌊11 (b)⌊10 (c)⌊11/2 (d)10×⌊11
T2
Book Problem 31 If the birth rate of a population is b(t) = 3600e0.034t people per year and the death rate is d(t) = 1530e0.014t people per year, then the increase in population over a 5-year period is equal to the area between these curves for 0 ≤ t ≤ 5. Thus, the increase in population during that period is equal to fodt =
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= 5. Prove that if x1 = 1 and xn+1 = V6 + xn, then xn <3 for all integers n > 1. e 6. Let E CR such that E is nonempty and bounded. Prove that the set -E ={-x : fies inf(E) = - sup(-E).