所屬科目：研究所、轉學考(插大)-微積分
1. =________
2. =________
3. If f(x) =, for x ∈ R, then f'(1) =________
4.=________
5.=________
6. The point on the curve y = x2 that is closest to the point (18, 0) is ________.
7. The area of the region outside the cardioid r = 1 + cosθ and inside the circle r = is ________
8.=________
9.=________
10. If f(x,y) =, then =________
二、計算題: 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 integral , where R is the trapezoidal region with vertices (1, 0), (2, 0), (0, -2), and (0, -1).
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=________
=________
, for x ∈ R, then f'(1) =________
=________
=________
is ________
=________
=________
, then 
=________
.
, where R is the trapezoidal region with vertices (1, 0), (2, 0), (0, -2), and (0, -1).