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107年 - 107 國立暨南大學轉學生招生考試試題_經濟系二、財金系二：微積分#123360

科目：研究所、轉學考(插大)-微積分 | 年份：107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)

1. Let f(x³ + x² + 2x + 1) = xex, Find f'(1) = ______
2.= ______
3. (x² - x) dx = ______ 
4. dx = ______ 
5. Evaluate the double integraldA= ______， where R = {(x,y)|0 ≤ x ≤ 2, x² ≤ y ≤ 4}.
6. Find the volume of the solid bounded above by the surface z = f(x, y) and  below by the plane region R. f(x, y) = ; R is the region bounded by  y = 9, y = 0, and x = 2.
Answer: ______
7. Suppose lim , Find a+b= ______
8. Let f(t) = . Find f''(2)= ______
9. Find an equation for the tangent line to the graph of f(x) = x ln at the point where x = 1. Answer: ______
10. Approximate the function f(x) = ln(x + 1) by a Taylor polynomial of degree 3 at x=0. Answer: ______
11. Determine the intervals where the function f(x) = is decreasing. Answer: ______
二、計算題 (共 12 分, 沒有列出計算過程者不予計分)
  1. (12%) Determine the intervals where the graph of the function f(x) = ln(x² + 1) is concave upward and where it is concave downward and find the inflection points of f.