104年 - 104 國立中正大學轉學生招生考試試題_共同科目：微積分#121936

選擇題 (4)

1. Which of the following must be true? (A)= 1 (B) If g(x) = |x-2|, thendoes not exist (C)tan^-1(1/x) does not exist (D) None of the above

2. Which of the following must be true? (A) The series converges (B) The seriesconverges absolutely (C) The seriesdiverges (D) None of the above

3. Let f(x, y) = x³ - 12xy + 8y³. Which of the following must be true? (A) f(x, y) has three critical points (B) (2,1) is a saddle point of f(x, y) (C) At the point P(1, 1), f(x, y) increases fastest in the direction (-3/5,4/5) (D) None of the above

4. Let C be a smooth curve defined by r(t) and C is also represented as r(s) in terms of the arc length parameter s. Which of the following must be true? (A) dr/ds = r'(t)dt (B) the unit tangent T = (C) the unit normal N = (D) None of the above

申論題 (10)

1. Let D be the region bounded by the parabola y = x² - x and the x-axis. Find the slope of the line passing through the origin that divides D into two regions with equal area.__(a)__

2. The following figure shows a unit circle in the first quadrant. At what height (h) above the x-axis should the horizontal line be placed so as to minimize the shaded area?__(b)__