Re: [考古] 高大96
※ 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.
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
等號兩邊同取ln
r*t = ln2
ln2
t = ----- years
r
有錯請指正
<(_._)>
: 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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