MA005: Calculus I

1. $5$

3. $0$

5. $3$

7. $0$

9. $-5$

11. $-5$

13. $0$

15. $4.5+5 = 9.5$

17. $10+3 = 13$

19. $5+2 = 7$

21. $1$

23. $-1$

25. $2.5$

27. $1$

29. $1$

31. (a) $8.6 = 48$          (b) $24$

33. (a) $32$                     (b) $8^{2}=64$

35. $8$

37. $2.5$

39. $3$

41. $7$

43.

(a) graph $\mathrm{y}=\mathrm{A}(\mathrm{x})=\mathrm{x}^{2} / 2$ 

(b) graph $y=A^{\prime}(x)=x$

45.

(a) graph of $\mathrm{y}=\mathrm{A}(\mathrm{x})$ in Figure 45a

(b) graph of $y=A^{\prime}(x)$ Figure 45b

47.

(a) $f$ is continuous on [1,4]

(b) $f$ is not differentiable on [1,4] (not diff. at $x \approx 2.3$ and $3.3$

(c) $f$ is integrable on [1,4]

49.

(a) $f$ is not continuous on [1,4] (not cont. at $x=2$ and $3$

(b) $f$ is not differentiable on [1,4] (not diff. at $x=2$ and $3$

(c) $f$ is integrable on [1,4]

51.$\int_{1}^{4} \text { velocity } \mathrm{dt}=\int_{1}^{2} \text { velocity } \mathrm{dt}+\int_{2}^{4} \text { velocity } \mathrm{dt}=35+50=85 \text{ miles}$