Calculus II, Spring 2024 (http://www.math.nthu.edu.tw/˜ wangwc/) Thomas’ Calculus Early Transcendentals 13ed

Study guide for Midterm 01

Midterm problems include both the lecture contents and homework problems.

1. Review study guide for quiz 01-05 (section 8.8, 10.1-10.8). In particular, pay attention to the items listed in the study guides but did not appear in the quizzes (due to time constraint).

2. Section 10.9: Study the statement of Taylor’s Theorem (Taylor’s formula). Study the Remainder Estimation Theorem and application on elementary functions.

3. Section 10.10: Memorize the binomial series and the Taylor series of basic functions in Table 10.1 (page 658). Study how to identify a function from its power series representation. Practice on variants of the functions in Table 10.1: Perform differentiation/integration on them and see if you can recognize the resulting new series. Then practice on examples such as section 10.10, problems 41-52 and Chap 10, Practice Exercises, problems 51-56.

4. Section 10.10: Review the application of Taylor series in

(a) Indeterminate forms (section 10.10, problems 29-40 and Chap 10, Practice Exercises, problems 73-79).

(b) Approximating functions and integrals and the error estimate (such as section 10.10, problems 15-28).