27: Section 7.4 Answers
- Page ID
- 103661
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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. \(y=c_1x+c_2x^2+c_3x^3+x\ln |x|\)
2. \(y=c_1\sqrt x+c_2{1\over \sqrt x}+c_3x^2+2x^{2}\ln |x|\)
3. \(y=c_1x+c_2x^2+c_3{1\over x}+\frac{x^{2}\ln |x|}{3}\)
4. \(y=c_1+c_2x+c_3x^2+c_4{1\over x}+\frac{1}{4}x^{3}\ln |x|-\frac{25}{48}x^{3}\)
5. \(y=c_1\sqrt x+c_2{1\over \sqrt x}+c_3x^{3/2}+c_4x^{-3/2}+\frac{x^{5/2}}{4}\)
6. \(y=c_1x+c_2x^2+c_3x^3+c_4x^4+\frac{x^{4}\ln |x|}{6}\)
7. \(y=c_1x+c_2x^2+c_3{1\over x}+c_4{1\over x^2}+x^{2}\ln |x|\)
8. \(y=-x(\ln x)^{2}+3x+x^{3}-2x\ln x\)
9. \(y=\frac{x^{3}}{2}(\ln |x|)^{2}+x^{2}-x^{3}+2x^{3}\ln |x|\)
10. \(y=\frac{3}{2}x^{4}(\ln x)^{2}+3x-x^{4}+2x^{4}\ln x\)
11. \(y=\left(\frac{x^{2}}{3}-\frac{x}{2}\right)\ln |x|+4x-2x^{2}\)
12. \(y=3x^{2}\ln x-7x^{2}\)
13. \(y=x\ln x+x-\sqrt{x}+\frac{1}{x}+\frac{1}{\sqrt{x}}\)
14. \(y=x^{3}\ln |x|+x-2x^{3}+\frac{1}{x}-\frac{1}{x^{2}}\)
15. \(y=c_1x+c_2x^2+c_3xe^x+2x^{3}\)
16. \(y=c_1e^{-x^2}+c_2xe^{-x^2}+c_3x^2e^{-x^2}+\frac{8}{105}x^{7/2}e^{-x^{2}}\)
17. \(y=c_1+c_2{e^x\over x}+c_3{e^{-x}\over x}-\frac{2(x^{2}+2)}{x}\)
18. \(y=c_1xe^x+c_2x^2e^x+c_3x^3e^x+-\frac{xe^{-3x}}{64}\)
19. \(y=c_1e^x+c_2e^{-x}+c_3{1\over x}-\frac{2x^{2}}{3}\)
20. \(y=c_1e^x+c_2{e^x\over x}+c_3{e^{-x}\over x}-\frac{e^{-x}(x+1)}{x}\)
21. \(y=c_1x+c_2{1\over x-1}+c_3{1\over x+1}+x^{2}+1\)
22. \(y=c_1x+c_2{1\over x}+c_3{e^x\over x}+\frac{2x^{2}+6}{3}\)
23. \(y=c_1x+c_2e^x+c_3e^{-x}-x^{2}-2\)
24. \(y=c_1+c_2{1\over x}+c_3e^x+c_4e^{-x}+\frac{x(12-x^{2})}{6}\)
25. \(y=c_1xe^x+c_2x^2e^x+c_3xe^{-x}+c_4x^2e^{-x}+\frac{x^{3}e^{x}}{2}\)
26. \(y=c_1e^x+c_2e^{-x}+c_3{e^x\over x}+c_4{e^{-x}\over x}+\frac{xe^{x}}{2}\)
27. \(y=c_1e^x+c_2e^{2x}+c_3{e^x\over x}+c_4{e^{2x}\over x}+\frac{3xe^{x}}{2}\)
28. \(y=c_1x+c_2x^2+c_3xe^x+c_4xe^{-x}-x^{3}\)
29. \(y=-\frac{1}{2}(3x+1)xe^{x}-3e^{x}-e^{2x}+4xe^{-x}\)
30. \(y=-\frac{x^{4}+12}{6}+3x-x^{2}+2e^{x}\)
31. \(y=-\frac{xe^{x}(1+3x)}{2}+\frac{x+1}{2}-\frac{e^{x}}{4}+\frac{e^{3x}}{2}\)
32. \(y=-8x+2x^{2}-2x^{3}+2e^{x}-e^{-x}\)
33. \(y=\frac{3(4x^{2}+9)}{2}+\frac{x}{2}-\frac{e^{x}}{2}+\frac{e^{-x}}{2}+\frac{e^{2x}}{4}\)