所屬科目：研究所、轉學考(插大)-微積分
1. (8 points) Evaluate
2. (8 points) Evaluate
3. (8 points) Evaluate
4. (8 points) Evaluate
5. (8 points) Let y = sin x - cos x. Find
8. (8 points) Evaluate
9. (8 points) Evaluate
10. (8 points)Find f(x) =
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
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, x≥ 0. Use the mean value theorem for definite integral and the limit-definition of derivative to find f'(x). 
(a,b) such that
[a,b] such that 