Solutions to Odd-Numbered Exercises

1. If $f$ is a polynomial function, the limit of a polynomial function as $x$ approaches $a$ will always be $f\left(a\right)$.

3. It could mean either (1) the values of the function increase or decrease without bound as $x$ approaches $c$, or (2) the left and right-hand limits are not equal.

5. $\frac{-10}{3}$

7. 6

9. $\frac{1}{2}$

11. 6

13. does not exist

15. $-12$

17. $-\frac{\sqrt{5}}{10}$

19. $-108$

21. 1

23. 6

25. 1

27. 1

29. does not exist

31. $6+\sqrt{5}$

33. $\frac{3}{5}$

35. 0

37. $-3$

39. does not exist; right-hand limit is not the same as the left-hand limit.

41. Limit does not exist; limit approaches infinity.

43. $4x+2h$

45. $2x+h+4$

47. $\frac{\cos \left(x+h\right)-\cos \left(x\right)}{h}$

49. $\frac{-1}{x\left(x+h\right)}$

51. $\frac{-1}{\sqrt{x+h}+\sqrt{x}}$

53. $f\left(x\right)=\frac{{x}^{2}+5x+6}{x+3}$

55. does not exist

57. 52