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研究所、轉學考(插大)-微積分
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110年 - 110東吳大學_碩士班招生考試_數學系A 組(數學)、數學系班 B 組(決策科學與海量資料分析) ︰微積分#100056
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6. (8 points) Let f(x)=xg(x),g(3)=5,and g'(3)= 2. Find f'(3).
其他申論題
2. (8 points) Evaluate
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3. (8 points) Evaluate
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4. (8 points) Evaluate
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5. (8 points) Let y = sin x - cos x. Find
#418909
7. (8 points) Let f'(x) = x√xand f(1) = 2. Find f(x).
#418911
8. (8 points) Evaluate
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9. (8 points) Evaluate
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10. (8 points)Find f(x) =
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11. (10 points) Let f'(x) exist everywhere. If f(2) = 8 and f'(x) ≤ 5 for all x. Use the mean value theorem to answer how small can f(0) possibly be?
#418915
12. (10 points) Let , x≥ 0. Use the mean value theorem for definite integral and the limit-definition of derivative to find f'(x). (Mean Value Theorem) Suppose f : [a,b] → IR is continuous on fa, b and differentiable on (a,b). Then there exists c (a,b) such that(Mean Value Theorem for Definite Integral) Suppose f : [a,b] → IR is a continuous function. Then there exists c [a,b] such that
#418916
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