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

Study guide for Midterm 02

Midterm problems include both the lecture contents and homework problems.

1. Review study guide for midterm 01. Review and correct your mistakes in midterm 01. Pay attention to algebraic manipulation, term by term differentiation and integration of power series, and identifying a function from its power series expansion. This part constitutes 15-20 extra points beyond the 100 points from Section 14.2-14.9.

2. Review study guide for quiz 06-09 (section 14.2-14.7). In particular, pay attention to the items listed in the study guides but did not appear in the quizzes (due to time constraint).

3. Section 14.8: Review all cases for the method of the Lagrangian multipliers. For example, extreme values of

• functions of 2 variables, with 1 constraint.

• functions of 3 variables, with 1 constraint.

• functions of 3 variables, with 2 constraints.

Pay attention to number of equations and number of unknowns in each case.

4. Section 14.9: Review the derivation of Taylor’s formula for functions of two variables and its generalization to three or more variables. Memorize the results.