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

7. The area of the region outside the cardioid r = 1 + cosθ and inside the circle r =sinθ is________.

8. ex+y dydx =_______.

9. sin(y²)dydx =___________.

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

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).

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

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)。