111年 - 111 台灣聯合大學系統(清華、交通、陽明、中央四校聯招)學士班轉學生考試：微積分#111207

科目：研究所、轉學考(插大)-微積分 | 年份：111年 | 選擇題數：0 | 申論題數：12

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (12)

1. Evaluate
Answer : __________

2. Find the volume of the smaller region cut from the solid sphere p ≤ 2 by the plane z = 1.
Answer :_________

3. Evaluate
Answer :___________

4. Evlate the iterated integral sin(y²)dydx.
Answer :_______

5.Find the area of the portion of the plane y + 2z = 2 inside the cylinder x²+ y²= 4.
Answer :___________

6. Suppose that F(x) is an antiderivative of dx in terms of F.
Answer : ____________

7. Along all triangles in the first quadrant formed by the a-axis, the y-axis, and tangent lines to the graph of y = 3x-x², what is the smallest possible area?
Answer :_____________

8. A space probe in the shape of the ellipsoid 4x²+ y²+4z² = 16 enters Earth's atmosphere and its surface begins to heat. After 1 hour, the temperature at the point (x,y, z) on the probe's surface is T(x, y, z) = 8x²+ 4yz - 16z + 600. Find the hottest point on the probe's surface.
Answer :____________

1. Find the Taylor polynomials of orders 2 generated by f(x) at a=0

2. Let a and b be constants with 0 ＜ a ＜ b. Does the sequence converge? If it does converge, what is the limit?

a. (6分)

b.(6分)