教甄教育專業科目-國小

(9).The area enclosed by the curves y =x3 and y = 9x is____

(10).The volume under the surface z 二 f(x,y) 二 y and over the domain D which is the region bounded b

二•計算題（共30分）必須寫出計算過程，否則不予計分.(1).(20%) Consider the function【題組】(a)(15%) Find all critical points，rela

【題組】(b)(5%) Sketch the graph.

(2).(10%) Evaluate the double integral

1. (20%)請簡述下列策略是否為差別取價？ if yes,為何種差別取價？【題組】a.遊樂圓的一票玩到底策略

【題組】b.冰箱的舊機換新機策略

【題組】c.航空公司機票週末加價策略

2. (20%) Suppose Lhat the T-account for First Nalional bank is as follows:【題組】(1)If Ihe central bank

【題組】(2)Assume tlial all olher banks hold only Ihe required amount of leserves. If Firsl Nalional ban

3. (20%) An economy is described by Ihe following equations【題組】a.Find the short run equilibrium outp

【題組】b.Find the governmenl purchase nmltiplier.

【題組】c.If ihe potential oulpul is 630. By how much would governmenl purchase have to change lo elimin

4.(20%)請說明政府對生產者生產課以從量稅的經濟效果.

5.(20%)請畫圖說明獨占廠商在短期時有虧損的狀態，並標明圖形上虧損的部分

【題組】d.計乘車夜間加成策略

1.Let M be the set consisting of m x n matrices with real entries.【題組】(a)Prove that is a vector spac

【題組】(b)Give a basis for A4 and find the dimension of M, (5%)

2.Let A be an n x n matrix with real entries. Let Wbe the null space of A, and let cbe a particular

3.Let T : U→ V and S : V →W be linear transformations. Prove that the

4.Prove or disprove each of the following statements.【題組】(a)If W and U are both subspaces of a vecto

【題組】(b)If W and U are both subspaces of a vector space V y thenis also a subspace of V (5%)

【題組】(c)det(A + D) =det(A)+dct(B), where clet(A) denotes the determinant of a square matrix A. (5%)

5.【題組】(a)Find the matrix representations of S、T and T o S relative to the standard basis.(6%)

【題組】(b)Find the matrix representations of S relative to the basis {(1，1)，(0, 2)}. (9%)

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