Chapter 5.3

Notes

Linguistic Mapping Exercises

Knowledge Checks

  1. Suppose that \((\theta_n)\) is a null sequence with only nonzero terms. Calculate \(\lim\limits_{n\to\infty} \tfrac{\sin(7\theta_n)}{5\theta_n}.\)
  2. Suppose that \((\theta_n)\) is a null sequence with only nonzero terms. Calculate \(\lim\limits_{n\to\infty} \tfrac{5-5\cos(2\theta_n)}{\theta_n}.\)
  3. Suppose that \((\theta_n)\) is a null sequence with only nonzero terms. Calculate \(\lim\limits_{n\to\infty} \tfrac{5-5\cos(2\theta_n)}{\theta_n^2}.\)
  4. 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.

Practice Problems

Return

© Copyright 2025 by the POC Writing Team: Bryan Carrillo, Yat Sun Poon, and David Weisbart. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the POC Writing Team.