110年 - 110 國立高雄大學_碩士班招生考試_統計學研究所(無組別)：微積分#102184

科目：研究所、轉學考(插大)-微積分 | 年份：110年 | 選擇題數：0 | 申論題數：10

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所屬科目：研究所、轉學考(插大)-微積分

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申論題 (10)

1. =？

2. Determine the open intervals of the x-axis on which the function
f(x) = 3x⁴ − 4x³ − 12x²+ 5 is increasing.

3. Show that

4. Find the area of the region bounded by the line y = x/2 and by the parabola
y² = 8 − x.

5. Evaluate the integral

6. Suppose that F(x) is an antiderivative of (sin x)/x, x ＞ 0. Express
In terms of F.

7. Show that

8. Determine

9. Find the Taylor series of

10. Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse