Section 1.2

1. $y (x) = x^{2} + x + 3$ $y (x) = x^{2} + x + 3$
2. $y (x) = \frac{1}{3} {(x - 2)}^{3} + 1$ $y (x) = \frac{1}{3} {(x - 2)}^{3} + 1$
3. $y (x) = \frac{1}{3} (2 x^{3/2} - 16)$ $y (x) = \frac{1}{3} (2 x^{3/2} - 16)$
4. $y (x) = - 1 / x + 6$ $y (x) = - 1 / x + 6$
5. $y (x) = 2 \sqrt{x + 2} - 5$ $y (x) = 2 \sqrt{x + 2} - 5$
6. $y (x) = \frac{1}{3} [{(x^{2} + 9)}^{3/2} - 125]$ $y (x) = \frac{1}{3} [{(x^{2} + 9)}^{3/2} - 125]$
7. $y (x) = 10 \tan^{- 1} x$ $y (x) = 10 \tan^{- 1} x$
8. $y (x) = \frac{1}{2} \sin 2 x + 1$ $y (x) = \frac{1}{2} \sin 2 x + 1$
9. $y (x) = \sin^{- 1} x$ $y (x) = \sin^{- 1} x$
10. $y (x) = - (x + 1) e^{- x} + 2$ $y (x) = - (x + 1) e^{- x} + 2$
11. $x (t) = 25 t^{2} + 10 t + 20$ $x (t) = 25 t^{2} + 10 t + 20$
12. $x (t) = - 10 t^{2} - 15 t + 5$ $x (t) = - 10 t^{2} - 15 t + 5$
13. $x (t) = \frac{1}{2} t^{3} + 5 t$ $x (t) = \frac{1}{2} t^{3} + 5 t$
14. $x (t) = \frac{1}{3} t^{3} + \frac{1}{2} t^{2} - 7 t + 4$ $x (t) = \frac{1}{3} t^{3} + \frac{1}{2} t^{2} - 7 t + 4$
15. $x (t) = \frac{1}{3} {(t + 3)}^{4} - 37 t - 26$ $x (t) = \frac{1}{3} {(t + 3)}^{4} - 37 t - 26$
16. $x (t) = \frac{4}{3} {(t + 4)}^{3/2} - 5 t - \frac{29}{3}$ $x (t) = \frac{4}{3} {(t + 4)}^{3/2} - 5 t - \frac{29}{3}$
17. $x (t) = \frac{1}{2} [{(t + 1)}^{- 1} + t - 1]$ $x (t) = \frac{1}{2} [{(t + 1)}^{- 1} + t - 1]$
19. $x (t) = {\begin{array}{l} 5 t & if 0 \leq t \leq 5, \\ 10 t - \frac{1}{2} t^{2} - \frac{25}{2} & if 5 \leq t \leq 10. \end{array}$ $x (t) = {\begin{array}{l} 5 t & if 0 \leq t \leq 5, \\ 10 t - \frac{1}{2} t^{2} - \frac{25}{2} & if 5 \leq t \leq 10. \end{array}$
20. $x (t) = {\begin{array}{l} \frac{1}{2} t^{2} & if 0 \leq t \leq 5, \\ 5 t - \frac{25}{2} & if 5 \leq t \leq 10. \end{array}$ $x (t) = {\begin{array}{l} \frac{1}{2} t^{2} & if 0 \leq t \leq 5, \\ 5 t - \frac{25}{2} & if 5 \leq t \leq 10. \end{array}$
21. $x (t) = {\begin{array}{l} \frac{1}{2} t^{2} & if 0 \leq t \leq 5, \\ 10 t - \frac{1}{2} t^{2} - 25 & if 5 \leq t \leq 10. \end{array}$ $x (t) = {\begin{array}{l} \frac{1}{2} t^{2} & if 0 \leq t \leq 5, \\ 10 t - \frac{1}{2} t^{2} - 25 & if 5 \leq t \leq 10. \end{array}$
22. $x (t) = {\begin{array}{l} \frac{5}{6} t^{2} & if 0 \leq t \leq 3, \\ 5 t - \frac{15}{2} & if 3 \leq t \leq 7, \\ \frac{1}{6} (- 5 t^{2} + 100 t - 290) & if 7 \leq t \leq 10. \end{array}$ $x (t) = {\begin{array}{l} \frac{5}{6} t^{2} & if 0 \leq t \leq 3, \\ 5 t - \frac{15}{2} & if 3 \leq t \leq 7, \\ \frac{1}{6} (- 5 t^{2} + 100 t - 290) & if 7 \leq t \leq 10. \end{array}$
23. $v (t) = - (9.8) t + 49$ $v (t) = - (9.8) t + 49$ , so the ball reaches its maximum height ( $v = 0$ $v = 0$ ) after $t = 5$ $t = 5$ seconds. Its maximum height then is $y (5) = 122.5$ $y (5) = 122.5$ (m).
24. $v (5) = - 160 ft/s$ $v (5) = - 160 ft/s$
25. The car stops when $t \approx 2.78 (s)$ $t \approx 2.78 (s)$ , so the distance traveled before stopping is approximately $x (2.78) \approx 38.58 (m)$ $x (2.78) \approx 38.58 (m)$ .
26. (a) $y \approx 530 m$ $y \approx 530 m$ (b) $t \approx 20.41 s$ $t \approx 20.41 s$ (c) $t \approx 20.61 s$ $t \approx 20.61 s$
27. $y_{0} \approx 178.57 (m)$ $y_{0} \approx 178.57 (m)$
28. $v (4.77) \approx - 192.64 ft/s$ $v (4.77) \approx - 192.64 ft/s$
29. After 10 seconds the car has traveled 200 ft and is traveling at 70 ft/s.
30. $a = 22 {ft/s}^{2}$ $a = 22 {ft/s}^{2}$ ; it skids for 4 seconds.
31. $v_{0} = 10 \sqrt{30} (m/s)$ $v_{0} = 10 \sqrt{30} (m/s)$ , about 197.18 km/h
32. 60 m
33. $20 \sqrt{10} \approx 63.25 (ft/s)$ $20 \sqrt{10} \approx 63.25 (ft/s)$
34. 460.8 ft
36. About 13.6 ft
37. 25 (mi)
38. 1:10 pm
39. 6 mph
40. 2.4 mi
41. $\frac{544}{3} \approx 181.33 (ft/s)$ $\frac{544}{3} \approx 181.33 (ft/s)$
42. 25 mi
43. Time: $6.12245 \times 10^{9} s \approx 194$ $6.12245 \times 10^{9} s \approx 194$ years;

Distance: $1.8367 \times 10^{17} m \approx 19.4$ $1.8367 \times 10^{17} m \approx 19.4$ light-years
44. About 54 mi/h

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Table of Contents for Section 1.2

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Table of Contents for
Section 1.2