32: Section 9.2 Answers
- Page ID
- 103652
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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. \({1\over 2}t^2\)
2. \({1\over 6}t^3\)
3. \(t-2t^4\)
4. \(4t-{2\over 3}t^3+{1\over 120}t^5\)
5. \(1+3t+{3\over 2}t^2+{1\over 6}t^3\)
6. \(1+4t+2t^2\)
7. \(t-1+e^{2t}\)
8. \(4+{1\over 4}t^4-e^{-8t}\)
9. \({1\over 4}e^{-t/4}\)
10. \({1\over 5}e^{2t/5}\)
11. \({5\over 7}\sin 7t\)
12. \(10\cos 4t\)
13. \(\cos {t\over 2}\)
14. \({1\over 2}\sin {t\over 2}\)
15. \(2\cos 3t-2\sin 3t\)
16. \(\cos \sqrt 2t+{\sqrt2\over 2}\sin \sqrt2t\)
17. \({1\over 3}-{1\over 3}e^{-3t}\)
18. \(-{1\over 4}+{5\over 4}e^{4t}\)
19. \({1\over 4}e^t+{3\over 4}e^{-3t}\)
20. \({1\over 9}e^{4t}-{1\over 9}e^{-5t}\)
21. \(0.3e^{0.1t}+0.6e^{-0.2t}\)
22. \(\cosh \sqrt3 t-\sqrt3\sinh \sqrt3t\)
23. \({1\over 2}e^{2t}-e^{3t}+{1\over 2}e^{6t}\)
24. \({1\over 2}-e^t-{1\over 3}e^{-t}+{5\over 6}e^{2t}\)
25. \({1\over 5}-{1\over 5}\cos \sqrt5t\)
26. \({1\over 4}\cos 2t+{1\over 4}\sin 2t-{1\over 4}e^{-2t}\)
27. \(-4+3e^{-t}+\cos t+3\sin t\)
28. \({1\over 6\sqrt3}\sinh \sqrt3t-{1\over 6\sqrt3}\sin \sqrt3t\)
29. \(2\cos t+\sin t-2\cos 2t-{1\over 2}\sin 2t\)
30. \(\frac{2}{3}\sin 3t\)
31. \(2\cos 3t+\frac{1}{3}\sin 3t\)
32. \(\cosh 3t+\frac{1}{3}\sinh 3t\)
33. \(1-\cos t\)
34. \(3\cosh t+4\sinh t\)
35. \(3e^{t}+4\cos 3t+\frac{1}{3}\sin 3t\)
36. \(\frac{1}{4}e^{2t}-\frac{1}{4}e^{-2t}-e^{-t}\)
37. \(\frac{1}{5}e^{-4t}-\frac{41}{5}e^{t}+5e^{3t}\)
38. \(-\frac{1}{2}e^{2t}-\frac{13}{10}e^{-2t}-\frac{1}{5}e^{3t}\)
39. \(-\frac{2}{5}e^{-4t}-\frac{3}{5}e^{t}\)
40. \(\frac{3}{20}e^{2t}-\frac{37}{12}e^{-2t}+\frac{1}{3}e^{t}+\frac{8}{5}e^{-3t}\)
41. \(\frac{39}{10}e^{t}+\frac{3}{14}e^{3t}+\frac{23}{105}e^{-4t}-\frac{7}{3}e^{2t}\)
42. \(\frac{4}{5}e^{-2t}-\frac{1}{2}e^{-t}-\frac{3}{10}\cos t+\frac{11}{10}\sin t\)
43. \(\frac{3}{5}\cos 2t+\frac{1}{5}\sin 2t-\frac{3}{5}\cos 3t-\frac{2}{15}\sin 3t\)
44. \(-\frac{4}{15}\cos t+\frac{1}{15}\sin t+\frac{4}{15}\cos 4t-\frac{1}{60}\sin 4t\)
45. \(\frac{5}{3}\cos t+\sin t-\frac{5}{3}\cos 2t-\frac{1}{2}\sin 2t\)
46. \(-\frac{1}{3}\cos \frac{t}{2}+\frac{2}{3}\sin\frac{t}{2}+\frac{1}{3}\cos t-\frac{1}{3}\sin t\)
47. \(\frac{1}{15}\cos\frac{t}{4}-\frac{8}{15}\sin\frac{t}{4}-\frac{1}{15}\cos 4t+\frac{1}{30}\sin 4t\)
48. \(\frac{2}{5}\cos\frac{t}{3}-\frac{3}{5}\sin\frac{t}{3}-\frac{2}{5}\cos\frac{t}{2}+\frac{2}{5}\sin\frac{t}{2}\)
49. \(1-\cos t\)
50. \(-\frac{3}{10}\sin t+\frac{2}{5}\cos t-\frac{3}{4}e^{t}+\frac{7}{20}e^{3t}\)
51. \(-\frac{1}{2}e^{t}+\frac{7}{10}e^{-t}-\frac{1}{5}\cos 2t+\frac{3}{5}\sin 2t\)