Let $$\(\mathrm{f}(x)=\frac{14-3 x+2 x^{2}}{(2+x)\left(3+x^{2}\right)}\)$$. Hence obtain the expansion of $$\(\mathrm{f}(x)\)$$ in ascending powers of $$\(x\)$$, up to and including the term in $$\(x^{2}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_32 Year：2021 Question No：9(b)
Answer:
Use correct method to find the first two terms of the expansion of \((2+x)^{-1}\),
\(\left(1+\frac{1}{2} x\right)^{-1},\left(3+x^{2}\right)^{-1} \text { or }\left(1+\frac{1}{3} x^{2}\right)^{-1}\)
Obtain correct unsimplified expansions up to the term in \(x^{2}\) of each partial fraction
Multiply out, up to the terms in \(x^{2}\), by \(B+C x\), where \(B C \neq 0\)
Obtain final answer \(\frac{7}{3}-\frac{5}{3} x+\frac{7}{18} x^{2}\)
\(\left(1+\frac{1}{2} x\right)^{-1},\left(3+x^{2}\right)^{-1} \text { or }\left(1+\frac{1}{3} x^{2}\right)^{-1}\)
Obtain correct unsimplified expansions up to the term in \(x^{2}\) of each partial fraction
Multiply out, up to the terms in \(x^{2}\), by \(B+C x\), where \(B C \neq 0\)
Obtain final answer \(\frac{7}{3}-\frac{5}{3} x+\frac{7}{18} x^{2}\)
Knowledge points:
3.1.5 use the expansion of , where n is a rational number and |x| < 1. (Finding the general term in an expansion is not included.) (Adapting the standard series to expand e.g. is included, and determining the set of values of x for which the expansion is valid in such cases is also included.)
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download