101年 - 101 國立高雄大學轉學生招生考試試題_電機工程學系：微積分#115937

科目：研究所、轉學考(插大)-微積分 | 年份：101年 | 選擇題數：0 | 申論題數：15

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 (15)

(a) y = 2^3x

(b) y=log₁₀ (3x²+ 4)

(c) y=x²e^−2x

(d) y= (ln x) /x

(e)

2. Find d²y/dx² / if x⁴+y⁴=16.

3. Evaluatedx.

4. Find the area enclosed by the line y=x−1 and the parabola y²=2x+6.

5. Find the volume of the solid obtained by rotating the region bounded by
y= x−x²and y = 0 about the line x = 2 .

6. Find the nth Taylor polynomial for about x =1.

(a) Find the area of the region in the first quadrant that is within the cardioid r =1 −cosθ .

(b) Find the entire area within the cardioid of (a).

8. Find the directional derivative of f (x,y,z)=x²y-yz³+z at the point (1, -2, 0) in the direction of the vector a .

9. Find the volume of the solid within the cylinder x²+y²= 9 and between the planes z =1 and x+z= 5.

10. Evaluate
along the circular arc C given by x = cos t , y= sin t (0≤t≤π/ 2).