救救我的微積分 研究所的題目

Question

use a fourth Maclaurin polynomial to approximate the value of ln(1.1)

solution because 1.1 is closer to 1 than to 0 you should consider Maclauri

n polynomials for the function g(x)=ln(1+x)

救救我的微積分吧!!

Answer 1

1/(1 x)=1-x x^2-x^3 x^4-... -1 同時積分得
ln(1 x)=x-x^2/2 x^3/3-x^4/4 .... -1 令x=0.1得ln(1.1)=0.1-0.01/2 0.001/3-0.0001/4+...

2007-11-28 16:05:24 補充：
加號都不見了,再補如下:
1/(1+ x)=1-x+ x^2-x^3+ x^4-... -1<1
同時積分得
ln(1+ x)=x-x^2/2+ x^3/3-x^4/4+ .... -1<=1
令x=0.1得ln(1.1)=0.1-0.01/2+ 0.001/3-0.0001/4+...