※ [本文轉錄自 Coming_EE 看板 #1PRVWGDU ]
作者: AUGnebulaUGA (去氧腺嘌呤核苷酸三磷酸) 看板: Coming_EE
標題: [考題] 106 微積分
時間: Tue Jul 18 19:59:10 2017
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.