所屬科目：研究所、轉學考(插大)-微積分
(a) If f '(0)=-1 , then =________.
(b) Let , then f (4)=________.
(c) =________.
(d) =________.
(e) =________.
(f) Let D ={(x , y )| x2+y2≤2 } , then ＝________.
(g) The derivative of function f ( x,y) at the point (1,1) in the direction toward (2,1) is 3 and in the direction toward (0,0) is , then the derivative of f at (1,1) in the direction toward the point (4,5) is ________.
2. Suppose that f is a continuous function satisfying Find f (3). （15 分）
（1）
（2） ，where [] means the Gaussian function.
（3）
（a）Evaluate
（b）Prove that
5. Prove that by Mean.Value.Theorem（10 分）
6. Find dx（10 分）
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=________.
, then f (4)=________.
=________.
=________.
=________.
＝________.
, then the derivative of f at (1,1) in the direction toward the point (4,5) is ________.
Find f (3). （15 分）
，where [] means the Gaussian function.
by Mean.Value.Theorem（10 分）
dx（10 分）