※ 引述《shallow1112 (小扯)》之銘言：
: 不好意思
: 有10題
: 麻煩大家了
: 謝謝
: 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.
: 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
(b)辛普森法則 (Simpson Rule)
將區間 [a,b] n等分 , n 為偶數 , 其等分點為 x_0 , x_1 , ... , x_n ,
x_0 = a , x_n = b , x_(n-1) , x_i , i = 1 , 2 , ... , n
(i)(b - a)
x_i = a + ---------- , i = 1 , 2 , ... , n
n
b
∫ f(x) dx
a
b - a
≒ (-----)(f(x_0)+f(x_n)+4(f(x_1)+f(x_3)+...+f(x_(n-1)))+
3n
2(f(x_2) + f(x_4) + ... + f(x_(n-2))))
x_0 = 1
(1)(3-1)
x_1 = 1 + -------- = 1.5
4
(2)(3-1)
x_2 = 1 + -------- = 2
4
(3)(3-1)
x_3 = 1 + -------- = 2.5
4
x_4 = 3
3
∫ (x+2)^3 dx
1
(3-1)
≒ (-----)(f(1)+f(3)+4*(f(1.5)+f(2.5))+2*f(2))
3*4
1
= (---)(3^3 + 5^3 + 4*((3.5)^3 + (4.5)^3) + 2*(4^3)) = 136
6
: 9.Find the Maclaurin sreies representation for f(x)=e^(-x^2) , then
: (49)
: find f (0).
: 10.John擬於下月1日向某車商購置一輛新車，車商現在有兩種優惠方案，一為現金價;
: 按原定價P元折抵X元(X<P)，一次付清;二為五年低利(年利率r)分期付款;依定價P元計
: 算，每月底還款Y元，試問John應如何比較此兩方案以節省荷包(假設五年內市場年利率
: 維持固定為i，且i>r)?
: 想請問一下
: 我有看到麥克勞林級數
: 請問這是會考的重點嗎???
: 還有大約考哪些重點呢?
: 我快嚇死了啦!我的天阿
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