推 s864372002 :考古題大集合嗎囧。 12/29 21:59
課程名稱︰微積分甲上
課程性質︰系內必帶
課程教師︰陳宏
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰2009/12/29
考試時限（分鐘）：50min
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
Make sure to give sufficient reason in each problem or you will NOT get any
credit for your answer.
1. (20 points) Let R be the region bounded above by y = 1 + sinx, 0<=x<=2πand
bounded below by x-axis. Rotate the region R about y-axis. Determine its
volume.
Solution: Refer to Q6 of 95 final.
http://www.math.ntu.edu.tw/~mathcal/download/exam/951A2Final.pdf
2. (20 points) Find the length of the curve |x|^(2/3)+|y|^(2/3)=1.
Solution: Refer to Q5 of 95 fianl.
http://www.math.ntu.edu.tw/~mathcal/download/exam/951A2Final.pdf
3. (20 points) Find the intersection of two curve r = cosθ and r = 1 - cosθ.
Solution: Refer to Q4(a) of 95 fianl.
http://www.math.ntu.edu.tw/~mathcal/download/exam/951A2Final.pdf
4. (20 points) Determine the hightest point on r = 1 + cosθ.
Solution: Refer to Q3 of 96 midterm.
http://www.math.ntu.edu.tw/~mathcal/download/exam/961A2(f)--solution.pdf
5. (20 points) Find the values of a for which the improper integral
∞ dx
∫ ------------- converges.
1 x^a (1+√x)
Solution: Refer to Q4(a) of 97 fianl.
http://www.math.ntu.edu.tw/~mathcal/download/exam/971A2finalsol.pdf
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