Chapter 5.3
\[ \definecolor{ucrblue}{rgb}{0.0627,0.3843,0.6039} \definecolor{ucrgold}{rgb}{0.9686,0.6941,0.2824} \definecolor{ucrred}{rgb}{0.8941,0,0.1686} \definecolor{ucrgreen}{rgb}{0.4706,0.7451,0.1255} \definecolor{ucraccent}{rgb}{1.0000,0.9569,0.8392} \DeclareMathOperator*{\LO}{O} \DeclareMathOperator*{\Lo}{o} \DeclareMathOperator*{\Recip}{Recip} \DeclareMathOperator*{\abs}{abs} \DeclareMathOperator{\pow}{pow} \]
Notes
Linguistic Mapping Exercises
Knowledge Checks
- Suppose that \((\theta_n)\) is a null sequence with only nonzero terms. Calculate \(\lim\limits_{n\to\infty} \tfrac{\sin(7\theta_n)}{5\theta_n}.\)
- Suppose that \((\theta_n)\) is a null sequence with only nonzero terms. Calculate \(\lim\limits_{n\to\infty} \tfrac{5-5\cos(2\theta_n)}{\theta_n}.\)
- Suppose that \((\theta_n)\) is a null sequence with only nonzero terms. Calculate \(\lim\limits_{n\to\infty} \tfrac{5-5\cos(2\theta_n)}{\theta_n^2}.\)
- Suppose that \((\theta_n)\) is a null sequence with only nonzero terms. Calculate \(\lim\limits_{n\to\infty} \tfrac{\tan(5\theta_n)}{\theta_n}.\)
Remember, do the knowledge checks before checking the solutions.