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625
²Ã Ý
2012 Ä
ÝÒß ÎÝ
¡Ê© Ï £ Ï ÓØ£ ±§ ¨Ú¥ ¼³¢
ÂÁ«¥ Ü Õ
℄¢ ¥´ ܦ¸ ܦ ¥ ¸¦¡¢ ܦ¨¬Ü¥
§ 150 2
1. (10 ) f(x) © [a, b] Ï Û É f(b) − f(a) = b − a, À
b
a
(f′
(x))2
dx ≥ b − a.
2. (10 ) ËÅÔÖ y = x2
°¯Ö x − y − 2 = 0 ƹ ¤
3. (10 ) Ë
∞
n=2
(−1)n xn
n(n−1)
¦¶° ¤
4. (10 ) ¸ µ I =
D
x2 + y2
4a2 − x2 − y2
dxdy, È D £ÍÖ
x2
+ y2
+ 2ay = 0 ¥¯Ö y = −x Р̦ (y > −x).
5. (10 ) ¸ µ L zdx +2xdy +3ydz, È L § x2
+y2
= a2
(a > 0) ¥Ç z = x + 1 ¼Ö£Æ z ¬× £ « פ
6. (10 ) ¸ µ S(y + z)2
dS, È S Ñ̦ (x, y, z)
√
y2 + z2 ≤
x ≤ 2} ©¾¤
7. (15 ) À f(x) = 1
x2 © (0, ∞) Ï Û ª Û¤
1
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