Calculus II, Spring 2019 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 10

1. Section 14.6: Problems 1, 9, 13, 19, 25, 33, 39, 45, 63. Remark: What problem 63 means is: Let L(x, y) = A(x − x_{0}) + B(y − y_{0}) + C be a linear function. Show that if L(x, y) satisfies

f(x, y) = L(x, y) + ε_{1}(x − x_{0}) + ε_{2}(y − y_{0})

(or f(x, y) = L(x, y) + ε\sqrt{(x − x_{0}^{2}) + (y − y_{0})^{2}}), where lim_{(x,y)→(x_{0},y_{0})} ε, ε_{1}, ε_{2} = 0. (In other words, if z = L(x, y) is a tangent plane at (x_{0}, y_{0}, f(x_{0}, y_{0})).) Then we must have

A = f_{x}(x_{0}, y_{0}), B = f_{y}(x_{0}, y_{0}), C = f(x_{0}, y_{0}).

2. Section 14.7: Problems 1, 19, 39, 51, 55.