112年 - 112 國立臺灣大學_碩士班招生考試:微積分(C)#114173

科目：台大◆企管◆微積分(C) | 年份：112年 | 選擇題數：0 | 申論題數：10

試卷資訊

所屬科目：台大◆企管◆微積分(C)

選擇題 (0)

申論題 (10)

(a) (10%) Given645d8b1e3bb04.jpg,express x= az1+β and γ=yz1 +δz2+εte such that 645d8b81c60cd.jpgWhat are a, β, γ, δ, and ε?

(b) (15%) Evaluate the expectation E[exp(x + y)I{x ≤ 0}], where I{A} is an indicator function returning 1 (0) ifthe condition A is true (false), and express the calculation result a +bn1(c;0,1)+dN1(e;0,1)+fn1(g:0,1)n1(h;0,1)+ in1(j；0,1)N1(k;0,1)+ IN2645d8c77ba4f3.jpg.What are a, b, c, d, e, f, g, h, i, j, k, I, m, and n?
(a) (10%) Solve both of these differential equations and express D(t) and I(t) in terms of a, r, l0, and D0.
(b) (5%) Determine what happens to this ratio in the long run by computing the limit
645d8ce62080f.jpg
3. (10%) IB company produces x units of commodity A and y units of commodity B. All the units can be sold for p = 20 - 5x dollars per unit of A and q = 4 - 2y dollars per unit of B. The cost (in dollars) of producing these units is given by the joint-cost function C(x,y) = 2xy + 4. What should x and y be to maximize profit?

4. (10%) Find 645d8d1073541.jpgfor the equation y3 +y2 -5y -x2 = -4.

5. (10%) Evaluate 645d8d3a1cfde.jpg dx.

6. (10%) Find the value of 645d8d53375e7.jpg(csc4x-cot4x)dx .

7. (10%) Use a Maclaurin polynomial to find the value of 645d8d8b3c9c8.jpg accurate to four decimal places.

8. (10%) Given f(x,y)= ex siny+ In xy, find 645d8da915ba8.jpg.