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91年 - 91 國立政治大學轉學生招生考試_應用數學系：微積分(一)#122828

科目：研究所、轉學考(插大)-微積分 | 年份：91年 | 選擇題數：0 | 申論題數：10

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 (10)

(a) Prove or disprove that f is one-to-one.
(b) Prove or disprove that f is onto.
(c) Prove or disprove that g is one-to-one.
(d) Prove or disprove that g is onto.

2. Use definition to show that 66ed13e56109f.jpg= 4.
3. Let f(x) = x5-x+1. Show that there is a number b such that f(b) = 10.

4. Given any real number r, show that 66ed14141cf8a.jpg.
5. Show that if f'(x) = 0 on an interval, then f is constant on that interval.
6. Show that if f''(x) ＞ 0 on an interval, then f is concave upward on that interval.

7. Let f be continuous on [a, b] and g(x) =66ed14408fbe7.jpg, a ≤ x ≤ b. Prove or disprove that g is differentiable on (a, b).