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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)

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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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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.
Transcribed Image Text: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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