Solution to Finding Limits: Properties of Limits

Solutions to Try Its

1. 26

2. 59

3. 10

4. [latex]-64[/latex]

5. [latex]-3[/latex]

6. [latex]-\frac{1}{50}[/latex]

7. [latex]-\frac{1}{8}[/latex]

8. [latex]2\sqrt{3}[/latex]

9. [latex]-1[/latex]

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