98年 - 98 國立中山大學轉學生招生考試試題_機電系二年級：微積分#122155

1. Find where y = f(t) dt.__(1)__.

2. At what points on the curve γ given by the equation y = x³ - 3x² + 2 is the tangent line parallel to the line y = 9x + 4?__(2)__

3. Determine I = ∫dx.__(3)__

4. Evaluate I = |1 - x²| dx.__(4)__

6. Find if x = t⁴ + t, y = t³ - t.__(6)__

7. Find the area A of the region interior to the right branch (x ≥ 0) of the curve described by the equation (x² + y²)² = a²(x² - y²), a ＞ 0.__(7)__

8. Determine the interval of convergence for the series __(8)__
S(x) = .

10. Find the average of the function f(x) = cos(t²) dt on the interval [0, 1].__(10)__