A.9.4: Section 9.4 Answers
- Page ID
- 43793
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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. \(y_{p}=2x^{3}\)
2. \(y_{p}=\frac{8}{105}x^{7/2}e^{-x^{2}}\)
3. \(y_{p}=x\ln |x|\)
4. \(y_{p}=-\frac{2(x^{2}+2)}{x}\)
5. \(y_{p}=-\frac{xe^{-3x}}{64}\)
6. \(y_{p}=-\frac{2x^{2}}{3}\)
7. \(y_{p}=-\frac{e^{-x}(x+1)}{x}\)
8. \(y_{p}=2x^{2}\ln |x|\)
9. \(y_{p}=x^{2}+1\)
10. \(y_{p}=\frac{2x^{2}+6}{3}\)
11. \(y_{p}=\frac{x^{2}\ln |x|}{3}\)
12. \(y_{p}=-x^{2}-2\)
13. \(\frac{1}{4}x^{3}\ln |x|-\frac{25}{48}x^{3}\)
14. \(y_{p}=\frac{x^{5/2}}{4}\)
15. \(y_{p}=\frac{x(12-x^{2})}{6}\)
16. \(y_{p}=\frac{x^{4}\ln |x|}{6}\)
17. \(y_{p}=\frac{x^{3}e^{x}}{2}\)
18. \(y_{p}=x^{2}\ln |x|\)
19. \(y_{p}=\frac{xe^{x}}{2}\)
20. \(y_{p}=\frac{3xe^{x}}{2}\)
21. \(y_{p}=-x^{3}\)
22. \(y=-x(\ln x)^{2}+3x+x^{3}-2x\ln x\)
23. \(y=\frac{x^{3}}{2}(\ln |x|)^{2}+x^{2}-x^{3}+2x^{3}\ln |x|\)
24. \(y=-\frac{1}{2}(3x+1)xe^{x}-3e^{x}-e^{2x}+4xe^{-x}\)
25. \(y=\frac{3}{2}x^{4}(\ln x)^{2}+3x-x^{4}+2x^{4}\ln x\)
26. \(y=-\frac{x^{4}+12}{6}+3x-x^{2}+2e^{x}\)
27. \(y=\left(\frac{x^{2}}{3}-\frac{x}{2}\right)\ln |x|+4x-2x^{2}\)
28. \(y=-\frac{xe^{x}(1+3x)}{2}+\frac{x+1}{2}-\frac{e^{x}}{4}+\frac{e^{3x}}{2}\)
29. \(y=-8x+2x^{2}-2x^{3}+2e^{x}-e^{-x}\)
30. \(y=3x^{2}\ln x-7x^{2}\)
31. \(y=\frac{3(4x^{2}+9)}{2}+\frac{x}{2}-\frac{e^{x}}{2}+\frac{e^{-x}}{2}+\frac{e^{2x}}{4}\)
32. \(y=x\ln x+x-\sqrt{x}+\frac{1}{x}+\frac{1}{\sqrt{x}}\)
33. \(y=x^{3}\ln |x|+x-2x^{3}+\frac{1}{x}-\frac{1}{x^{2}}\)
35. \(y_{p}=\int_{x_{0}}^{x}\frac{e^{(x-t)}-3e^{-(x-t)}+2e^{-2(x-t)} }{6}F(t)dt\)
36. \(y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{2}(2x+t)}{6xt^{3}}F(t)dt\)
37. \(y_{p}=\int_{x_{0}}^{x}\frac{xe^{(x-t)}-x^{2}+x(t-1) }{t^{4}}F(t)dt\)
38. \(y_{p}=\int_{x_{0}}^{x}\frac{x^{2}-t(t-2)-2te^{(x-t)}}{2x(t-1)^{2}}F(t)dt\)
39. \(y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}-2e^{(x-t)}+2e^{-(x-t)}-e^{-2(x-t)}}{12}F(t)dt\)
40. \(y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{3}}{6x}F(t)dt\)
41. \(y_{p}=\int_{x_{0}}^{x}\frac{(x+t)(x-t)^{3}}{12x^{2}t^{3}}F(t)dt\)
42. \(y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}(1+2x)+e^{-2(x-t)}(1-2t)-4x^{2}+4t^{2}-2}{32t^{2}}F(t)dt\)