1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise ofMin(S) and Max(S).2n(b) Let B =: neNЗп + 11i. Prove that inf B2ii. Show sup B3(c) If x, y E R such that x > 0 and y > 0. Using the fact that , Vx E R, x² > 0,prove each of the following.1(x + y).i.2ii. xy < (x2 + y²).iN

a) The given set is,S=n-1n:n∈ℕ

1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). 2n (b) Let B = : ne { 3n + 1° "€N. 1 i. Prove that inf B 2 2 ii. Show sup B 3 (c) If x, y E R such that r > 0 and y > 0. Using the fact that , V x ER, x2 > 0, prove each of the following. i. Vry < 1 (x + y) . ii. xy < (2² + y²) .

1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). 2n (b) Let B = : ne { 3n + 1° "€N. 1 i. Prove that inf B 2 2 ii. Show sup B 3 (c) If x, y E R such that r > 0 and y > 0. Using the fact that , V x ER, x2 > 0, prove each of the following. i. Vry < 1 (x + y) . ii. xy < (2² + y²) .

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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Question

100%

1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of
Min(S) and Max(S).
2n
(b) Let B =
: neN
Зп + 1
1
i. Prove that inf B
2
ii. Show sup B
3
(c) If x, y E R such that x > 0 and y > 0. Using the fact that , Vx E R, x² > 0,
prove each of the following.
1
(x + y).
i.
2
ii. xy < (x2 + y²).
iN

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