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研究所、轉學考(插大)-高等微積分
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107年 - 107 東吳大學_碩士班招生考試_數學系(A組)：高等微積分#107433
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題組內容
3. (20%)
(b) Find ∂
x
f , ∂
y
f and determine whether ∂
x
f (0,0) and ∂
y
f (0,0) exist or not.
其他申論題
(a) If a sequence in R n is convergent, then it is Cauchy.
#460128
(b) The function f ( x ) = cos x + x is uniformly continuous on .
#460129
2.(20%) Suppose that f is three times differentiable on an interval containing a . Show that Can you find the generalization to higher derivatives?
#460130
(a) Prove that f is not continuous at (0, 0) .
#460131
4.(15%) Suppose that f is a homogeneous function of degree a on R n .That is, . Show that ( f is twice differentiable)
#460133
(a)
#460134
(b)Let S = {( x, y ) : 0 ≤ y ≤ 2, y / 2 ≤ x ≤ 1} . EvaluatedA
#460135
(c) Let S = {( x, y ) : y ≥ 0, x 2 + y 2 ≤ 1} . EvaluatedA
#460136
一、在其他條件不變之下，試說明下列事件發生後，對羊毛的需求或供給的影響： (一)羊毛價格下跌。（5 分）
#460137
(二)羊毛衣價格下跌。（5 分）
#460138
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