2: Section 1.2 Answers
- Page ID
- 103601
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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. a. \(x_{0}\neq k\pi \;\;\;\;(k=\text{integer})\); all \(y_0\)
b. \(x_{0}\neq k\pi \;\;\;\;(k=\text{integer})\); all \(y_0\)
2. a. all \((x_0,y_0)\)
b. all \(x_0\); all \(y_0\ne 0\)
3. a. \(x_{0}y_{0}\neq (2k+1)\frac{\pi }{2} \;\;\;\; (k=\text{integer})\)
b. \(x_{0}y_{0}\neq (2k+1)\frac{\pi }{2} \;\;\;\; (k=\text{integer})\)
4. a. \(x_{0}y_{0}>0\text{ and }x_{0}y_{0}\neq 1\)
b. \(x_{0}y_{0}>0\text{ and }x_{0}y_{0}\neq 1\)
5. a. all \((x_{0},y_{0})\)
b. \((x_{0},y_{0})\) with \(y_{0}\neq 0\)
6. a. all \((x_{0}, y_{0})\)
b. all \((x_{0}, y_{0})\)
7. a. all \(x_0\) with \(y_{0}\neq\pm 2\)
b. all \(x_0\) with \(y_{0}\neq\pm 2\)
8. a. all \((x_{0}, y_{0})\)
b. all \((x_{0}, y_{0})\)
9. a. \((x_{0}, y_{0})\) such that \(x_{0}\neq 4y_{0}\)
b. \((x_{0}, y_{0})\) such that \(x_{0}\neq 4y_{0}\)
10. a. all \((x_{0}, y_{0})\)
b. \( (x_{0},y_{0})\neq (0,0)\)
11. a. all \((x_{0}, y_{0})\)
b. all \((x_{0}, y_{0})\) with \(y_{0}\neq\pm 1\)
12. a. all \((x_{0}, y_{0})\)
b. all \((x_{0}, y_{0})\)
13. a. all \((x_{0}, y_{0})\) such that \(y_0 > -x_0\)
b. all \((x_{0}, y_{0})\) such that \(y_0 > -x_0\)
14. a. all \((x_{0}, y_{0})\) with \(x_{0}\neq 1,\quad y_{0}\neq (2k+1)\frac{\pi }{2}(k=\text{integer})\)
b. all \((x_{0}, y_{0})\) with \(x_{0}\neq 1,\quad y_{0}\neq (2k+1)\frac{\pi }{2}(k=\text{integer})\)
15. a. all \((x_{0}, y_{0})\)
b. all \((x_{0}, y_{0})\) with \(y_{0}\neq 1\)
16. a. yes, \(y=0\)
b. no, \(y=x^3\)
17. d. \(y=-{1\over x-1}\) on \((-\infty,1)\)
e. \(y=-{1\over x+1}\) on \((-1,\infty)\)
f. \(y=0\) on \((-\infty,\infty)\)
18. d. \(y=\tan(x+{\pi\over 4})\) on \((-{3\pi\over 4},{\pi\over 4})\)