V. Composition (30%)
Write a 300-word essay on how to enjoy doing nothing.

10. If f(x, y) = (sin x)y, then =__________.

1. Find the radius and interval of convergence for the series .

2. Find all relative extrema and saddle points of f(x, y) = x² + y⁴ – 4xy + 1.

3. Find the integraldA , where R is the trapezoidal region with vertices (1, 0), (2, 0), (0, −2), and (0, −1).

IV. Composition writing: 30%The 85 richest people on Earth... are a small part of the richest 1% of the population, which combined owns about 46% of global wealth, according to the report from British humanitarian group Oxfam International.(from Los Angeles Times, January 20, 2014)Based on the given report, please write a paragraph of 300 words to discuss the problem of income inequality in Taiwan and offer your suggestion(s) to improve this situation in Taiwan.

1. (10%) 考慮以「o」表示「是」、「×」表示「否」,填入下表:

(a) 令f(x) = x5 + 2x3 + 2x, 且 f-1(x) 代表 f(x) 之反函數, 求 (f-1)'(-5)。

(b) 已知2y2 = 28 - x2 + xy, 求在 (x,y) = (-2,-4) 之值。

(c) 求積分dx。

(d) 求積分∫x cos x dx.