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研究所、轉學考(插大)-高等微積分
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97年 - 97 淡江大學 轉學考 高等微積分#55794
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題組內容
5. Letf(x, y)= (xy ,x
2
+ y
2
).
(1). Show that g=f
-1
exists and is differentiable in some nonempty open set containing (2,5). (10 points)
其他申論題
【已刪除】1. Show that t(x) = is not uniformly continuous on (0,1). (10 points).
#210893
【已刪除】2.
#210894
【已刪除】3. Iff: R is differentiable and i = f(x-y), show that=0.(10 points)
#210895
4. Let K be a compact subset of R and let f be a real —vaiued function on K. Prove that if f is continuous on K, then f (K) is compact. (10 points)
#210896
(2). Find Dg(2，5)(the total derivative ofg at(2,5)). (10 points)
#210898
【已刪除】6. Let f be continuous on [a, b]. Show that A in [a, b] if and only iff(x) = 0 for all x in[a，b]. (15 points)
#210899
【已刪除】7. Let t : [0, l]→[0，1] be continuous. Prove that there is c [0，11 sucli that f(c)=c. (10 points)
#210900
【已刪除】8. (5 points)
#210901
9. Let {fn} be a sequence of real-vaiued functions on [0，l] and fn converges uniformly to a function f. Prove that if each fn is continuous on [0,1], then f is continuous on [0,1]. (10 points)
#210902
I - Given Ihe following information about llie markeis of an economy: (25 分）
#210903
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