I need help with #2 and #3. Thank you. 1. Prove or give counterexample.(a) If (xn) and (Yn) diverge, then (xn + Yn) diverges.(b) If (x„) and (Yn) diverge, then („Yn) diverges.(c) If (xn) and (Tn + Yn) converge, then (yn) converges.(d) If (x„) and („Yn) converge, then (yn) converges.COs n2. Use the definition of convergence to prove lim= 0n+0 n2 – n +13. Calculate the following limit analytically using theorems from the notes.lim (Vn² + n – n)4. Let xn → 0 and (yn) be bounded. Prove xnYn → 0.5. Prove that r € E' iff there exists a sequence (xn) in E\{x} such that x, → r.

I am using the definition and bounness of cos functions and with the help of Archimedean property i…

Answered: COs n 2. Use the definition of…

COs n 2. Use the definition of convergence to prove lim n-0 n2 - n+ 1 3. Calculate the following limit analytically using theorems from the notes. lim (Vn² + n – n)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 76E

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Question

I need help with #2 and #3. Thank you.

1. Prove or give counterexample.
(a) If (xn) and (Yn) diverge, then (xn + Yn) diverges.
(b) If (x„) and (Yn) diverge, then („Yn) diverges.
(c) If (xn) and (Tn + Yn) converge, then (yn) converges.
(d) If (x„) and („Yn) converge, then (yn) converges.
COs n
2. Use the definition of convergence to prove lim
= 0
n+0 n2 – n +1
3. Calculate the following limit analytically using theorems from the notes.
lim (Vn² + n – n)
4. Let xn → 0 and (yn) be bounded. Prove xnYn → 0.
5. Prove that r € E' iff there exists a sequence (xn) in E\{x} such that x, → r.

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