※ 引述《shallow1112 (小扯)》之铭言： : 不好意思 : 有10题 : 麻烦大家了 : 谢谢 : 1.A Deposit $P made into a fund with an annual interest rate of r : . Fund the time (in years) necessary to double if the interest is : compounded continuously. dx ---- = r*x , x(0) = P dt dx ---- = r dt x ln(x) = r*t + c t = 0 , x = P 代入上式 ln(P) = 0 + c = c ln(x) = r*t + ln(P) = ln((P)(e^(r*t))) x = (P)(e^(r*t)) (P)(e^(r*t)) = 2P e^(r*t) = 2 等号两边同取ln r*t = ln2 ln2 t = ----- years r 有错请指正 <(_._)> : 2.determine the convergence or divergence for the following series: : ∞ n! ∞ n! : (a)Σ －－－ (b)Σ －－－ : n=1 n^n n=1 10^n : 3.For what values of η (demand elasticity of price, η>0) is the : demand function p=37x^(-1/η) elastic, where p is the price of x? : x-4 : 4.Find all intervals of x on which y=------- is concave down. : x+4 : dy siny : 5.Find ---- for y^3+------=㏑√cosx +4x : dx e^y : 6.Find the area of the region bounded by the graphs of y=x^2 and y=2-x^2. : 7.Find the integral ∫e^3xsin4xdx. : 8.Please use (a) Trapezoidal rule, and (b) Simpson rule both with n=4 to : 3 : approximate ∫ (x+2)^3 dx. : 1 : 9.Find the Maclaurin sreies representation for f(x)=e^(-x^2) , then : (49) : find f (0). : 10.John拟於下月1日向某车商购置一辆新车，车商现在有两种优惠方案，一为现金价; : 按原定价P元折抵X元(X<P)，一次付清;二为五年低利(年利率r)分期付款;依定价P元计 : 算，每月底还款Y元，试问John应如何比较此两方案以节省荷包(假设五年内市场年利率 : 维持固定为i，且i>r)? : 想请问一下 : 我有看到麦克劳林级数 : 请问这是会考的重点吗??? : 还有大约考哪些重点呢? : 我快吓死了啦!我的天阿 --

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