[考題] 106 微積分

[AUGnebulaUGA (去氧腺嘌呤核苷酸三磷酸)]

 1. (10%) Find lim_{x->2} (x^3-8)/(x^2-4).


 2. (10%) Show that x(t)=abs{t*sin(t)/(t^2+2)} is continuous for every number

          of x.


 3. (10%) Find df(t)/dt if f(t)=(t-1)(t^2-2t)/t^4.


 4. (10%) Graph the function y=x+1/x on x-y plane.


 5. (10%) Estimate f(1) if df(x)/dx=1/(5-x^2) and f(0)=2.


 6. (10%) Find dy/dx if y=int_{0}^{x^2} cos(t) dt.


 7. (10%) Find the inverse of: y=1/4*x+3.


 8. (10%) Evaluate int_{1}^{4} 1/(sqrt{x}(1+sqrt{x}) dx.


 9. (10%) Evaluate int_{0}^{pi/2} cos^4(x)sin^3(x) dx.


10. (10%) Find the Maclaurin series of sin(x). Prove that the series equal to

          sin(x) for all x.

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話說這張考卷的排版真的超不整齊的有失專業 =^=

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※ 編輯: AUGnebulaUGA (140.112.249.124), 07/18/2017 19:59:57
※ 編輯: AUGnebulaUGA (140.112.249.124), 07/18/2017 20:03:18
推 l061182: 推 考題很像剪下貼上的
※ AUGnebulaUGA:轉錄至看板 DoubleMajor                             07/18 20:19
推 loverTH: 今年水水
推 yuanyuan0123: 第一題分子分母反了
感謝指正~
※ 編輯: AUGnebulaUGA (140.112.249.124), 07/19/2017 14:40:47
推 JI1: 4.7500000