Calculus II, Spring 2016 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 09

1. Section 14.6: Problems 1, 9, 13, 19, 25, 33, 39, 45, 59, 63, 66, 67.

2. Section 14.7: Problems 1, 19, 43, 44, 49, 51, 55.

3. Section 14.9: Problems 7, 9, 11.

4. Taylor’s formula for functions of 2 variables can be summarized as

f(x_{0} + Δx, y_{0} + Δy) = f(x_{0}, y_{0}) + ∑_{k=1}^{n} \frac{1}{k!}(Δx∂_{x} + Δy∂_{y})^{k}f(x_{0}, y_{0})

+\frac{1}{(n + 1)!}(Δx∂_{x} + Δy∂_{y})^{n+1}f(x_{0} + cΔx, y_{0} + cΔy), 0 < c < 1.

Derive a similar formula for functions of 3 variables.