97年 - 97 國立政治大學轉學生招生考試_應用數學系：微積分(二)#122385

科目：研究所、轉學考(插大)-微積分 | 年份：97年 | 選擇題數：0 | 申論題數：11

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 (11)

(a) (10%)dx

(b) (10%)

(a) (10%) Find the Maclaurin series for arctan x.

(b) (5%) Find the interval of convergence of the Maclaurin series in (a). (Be sure to include a check for convergence at the endpoints of the interval.)

(c) (5%) Using the results in (a) and (b), find a series to calculate π.

(a) (5%) ∫[ln(x)]² dx

(b) (5%) ∫csc(θ) dθ

4. (10%) Evaluate the limit

5. (10%) Find the total length of the curve r = 2(l + cos θ).

6. (15%) Find the volume common to two solid cylinders, each with radius r, where the cylinders intersect at right angles.

7. (15%) Find a function f and a number a such that

for all x ＞ 0.