94年 - 94 國立臺灣師範大學_學士班轉學生招生考試試題_地球科學系二年級：微積分#122375

科目：研究所、轉學考(插大)-微積分 | 年份：94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)

(a) [(x² + 1)⁴] = ?

(b) ∫ e^xcosx dx = ?

(c)= ?

(d) dx = ?

(a) (f⁻¹∘g⁻¹)(1) = ?

(b) (g⁻¹∘f⁻¹)(-3) = ?

3. Find the equation of the tangent line to the graph given by x²(x² + y²) = y² at the point (). (10 分)

4. A baseball diamond has the shape of a square with 60 feet long. A player running from second base to third base at a speed of 15 feet per second is 45 feet from third base. At what rate is the distance between the player and the home plate changing? (10 分)

5. Find the interval of convergence of the series. (10 分)

6. Prove that if converges absolutely then it converges. Is the converse true? Show it or give a counterexample. (12 分)

7. Find the area of the surface generated by revolving about
the x-axis the graph of y = sinx from x=0 to x=π/2. (10 分)

8. Find the area of the region common to the two regions bounded by the following curves: r = -6cosθ, r = 2 - 2cosθ. (10 分)