28: Section 8.2 Answers
- Page ID
- 103644
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. \(R = 2;\: I = (−1, 3)\)
2. \(R = 1/2;\: I = (3/2, 5/2)\)
3. \(R = 0\)
4. \(R = 16;\: I = (−14, 18)\)
5. \(R = ∞;\: I = (−∞, ∞)\)
6. \(R = 4/3;\: I = (−25/3, −17/3)\)
7. \(R = 1;\: I = (0, 2)\)
8. \(R = \sqrt{2};\: I = (−2 −\sqrt{2}, −2 + \sqrt{2})\)
9. \(R = ∞;\: I = (−∞,∞)\)
10. \(R = 0\)
11. \(R = \sqrt{3};\: I = (− \sqrt{3}, \sqrt{3})\)
12. \(R = 1;\: I = (0, 2)\)
13. \(R = 3;\: I = (0, 6)\)
14. \(R = 1;\: I = (−1, 1)\)
15. \(R = 1/\sqrt{3};\: I = (3 − 1/\sqrt{3}, 3 + 1/\sqrt{3})\)
16. \(R = ∞;\: I = (−∞, ∞)\)
17. \(R = 0\)
18. \(R = 2;\: I = (−1, 3)\)
19. \((4a_2+3a_0)+\sum_{n=1}^\infty [2(n + 2)(n + 1)a_{n+2} + (n + 1)na_{n+1} + (n + 3)a_{n}]x^n\)
20. \((2a_2-2a_0)+(6a_3-2a_1)x+\sum_{n=2}^\infty [( n + 2)(n + 1)a_{n+2} + [3n(n − 1) − 2]a_{n} + 3(n − 1)a_{n−1}]x^n\)
21. \((2a_2-a_1+4a_0)+(6a_3+4a_2+4a_1)x+\sum_{n=2}^\infty [(n + 2)(n + 1)a_{n+2} + 2(n + 1)a_{n+1} + (2n^{2} − 5n + 4)a_{n}]x^n\)
22. \((2a_2+2a_1+3a_0)+(6a_3+4a_2+2a_1)x+\sum_{n=2}^\infty [(n + 2)(n + 1)a_{n+2} + 2(n + 1)a_{n+1} + (n^{2} − 2n + 3)a_{n}]x^n\)
23. \((2a_2+4a_0)+(6a_3+2a_1)x+\sum_{n=2}^\infty [(n + 2)(n + 1)a_{n+2} + (3n^{2} − 5n + 4)a_{n}]x^n\)
24. \((-2a_2+2a_1+a_0)+\sum_{n=1}^\infty [−(n + 2)(n + 1)a_{n+2} + (n + 1)(n + 2)a_{n+1} + (2n + 1)a_{n} + a_{n−1}](x+1)^n\)
25. \((8a_2+4a_1-6a_0)+(24a_3+16a_2-4a_1-3a_0)(x-2)+\sum_{n=2}^\infty [4(n + 2)(n + 1)a_{n+2} + 4(n + 1)^{2}a_{n+1} + (n^{2} + n − 6)a_{n} − 3a_{n−1}](x-2)^n\)