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

Study guide for quiz 08

Quiz problems include both the lecture contents and homework problems.

1. Section 14.4: Study the Chain rule for composition of differentiable functions of one or more independent variables (along with one or more intermediate variables) such as Theorem 5 (1 independent, 2 intermediate variables), Theorem 6 (1 independent, 3 intermediate variables), Theorem 7 (2 independent, 3 intermediate variables) and so on for more general cases.

2. Section 14.4: Study how to evaluate

\frac{d}{dx} ∫_{g_{1}(x)}^{g_{2}(x)} f(x, t) dt.

3. Section 14.5: Study the definition of directional derivative and how to compute it from definition, and alternatively how to compute it using partial derivatives when the function is differentiable.

4. Section 14.5: Study the geometric meaning of the gradient vector. Study how to find the tangent line and normal line of a level curve of f(x, y) (i.e., {(x, y) | f(x, y) = c}) using gradient of f.