Math 3A Demonstration 4

\[ \definecolor{ucrblue}{rgb}{0.0627,0.3843,0.6039} \definecolor{ucrgold}{rgb}{0.9686,0.6941,0.2824} \definecolor{ucrred}{rgb}{0.8941,0,0.1686} \definecolor{ucrgreen}{rgb}{0.4706,0.7451,0.1255} \definecolor{ucraccent}{rgb}{1.0000,0.9569,0.8392} \DeclareMathOperator*{\LO}{O} \DeclareMathOperator*{\Lo}{o} \DeclareMathOperator*{\Recip}{Recip} \DeclareMathOperator*{\abs}{abs} \DeclareMathOperator{\pow}{pow} \]

Demonstration Instructions

Make sure your face is visible in the video. At the bare minimum, you should show your face at the beginning and introduce yourself verbally so that I know that it is you doing the Demonstration assignment.

Questions

1. Pick one question from the [Q] Chapter 5.2 Online Assignment to explain how you get the correct answer.
2. Pick a different question from the [Q] Chapter 5.2 Online Assignment to explain how you get the correct answer.
3. Use Exercise 2 from the Chapter 5.2 Linguistic Mapping Exercises as a guide to use the Archimedean property of \(\mathbb{R}\) to show that \((a_n)\) is a null sequence, where \((a_n)\) is given by \[a_n=\frac{1}{5n+3}.\] and the determine the area of \(R\).
4. Explain why the following limit is of indeterminant form \[\lim_{n\to\infty}\frac{5n^2+2n-1}{n^2-n+7}.\] Then rewrite it in order to evaluate the limit using the limit laws.

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