2: Section 1.2 Answers

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 \((-{3\pi\over 4},{\pi\over 4})\)

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