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

Homework Assignment for Week 08

1. Section 14.5: Problems 9, 15, 19, 25, 27, 29, 35, 36, 40 (See page 807).

2. Let f(x, y) = x^{2}y/(x^{2} + y^{2}) for (x, y) ≠ (0, 0) and f(0, 0) = 0. (a) Is f continuous at (0, 0)?

(b) Do f_{x} and f_{y} exist at (0, 0)?

(c) Evaluate the directional derivative of f at (x_{0}, y_{0}) = (0, 0) in the direction (cos θ, sin θ), i.e. df/ds_{(cos θ,sin θ),(0,0)}, if it exists.

(d) Is f differentiable at (0, 0)?