(a) Expand (1-2x)^(2/3) in ascendin powers of x as far as the term containing x^3 for
-1<1
(b) Using the expansion in (a), find the values of 81^(1/3)correct to 4 significant figures
General Binomial Series
2007-10-13 8:03 pm
回答 (1)
2007-10-13 9:49 pm
✔ 最佳答案
(a)(1-2x)^(2/3)
=1-(2/3 1)(2x)+(2/3 2)(2x)^2-(2/3 3)(2x)^3
=1-(2/3)(2x)+(2/3)(-1/3)(1/2)(4x^2)-(2/3)(-1/3)(-4/3)(1/6)(8x^3)
=1-(4/3)x-(4/9)x^2-(32/81)x^3+...
(b)
sub x=4/9 in (1-2x)^(2/3)
(1/9)^(2/3)
=1-(4/3)(4/9)-(4/9)(4/9)^2-(32/81)(4/9)^3+...
=0.2849
So
81^(1/3)
=9^(2/3)
=1/0.2849
=3.5100 (correct to 4 significant figures )
The true value of 81^(1/3) is 4.3267
收錄日期: 2021-04-13 18:13:50
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071013000051KK01485