Solutions to Odd-Numbered Exercises
1. If [latex]f[/latex] is a polynomial function, the limit of a polynomial function as [latex]x[/latex] approaches [latex]a[/latex] will always be [latex]f\left(a\right)[/latex].
3. It could mean either (1) the values of the function increase or decrease without bound as [latex]x[/latex] approaches [latex]c[/latex], or (2) the left and right-hand limits are not equal.
5. [latex]\frac{-10}{3}[/latex]
7. 6
9. [latex]\frac{1}{2}[/latex]
11. 6
13. does not exist
15. [latex]-12[/latex]
17. [latex]-\frac{\sqrt{5}}{10}[/latex]
19. [latex]-108[/latex]
21. 1
23. 6
25. 1
27. 1
29. does not exist
31. [latex]6+\sqrt{5}[/latex]
33. [latex]\frac{3}{5}[/latex]
35. 0
37. [latex]-3[/latex]
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. [latex]4x+2h[/latex]
45. [latex]2x+h+4[/latex]
47. [latex]\frac{\cos \left(x+h\right)-\cos \left(x\right)}{h}[/latex]
49. [latex]\frac{-1}{x\left(x+h\right)}[/latex]
51. [latex]\frac{-1}{\sqrt{x+h}+\sqrt{x}}[/latex]
53. [latex]f\left(x\right)=\frac{{x}^{2}+5x+6}{x+3}[/latex]
55. does not exist
57. 52