1. Review Problems Chapter 5.1 – 5.7

2. Review Problems
Find the domain of the function: f(x) = ln(3x + 1).

3. Review Problems
Find the domain of the function: f(x) = 3 + ln(x - 1).
(1, )

4. Review Problems Match the graph with the correct function
[A] f(x) = ln x
[B] f(x) = ex-1
[C] f(x) = ln(x - 1)
[D] f(x) = ex
Review Problems
Match the graph with the correct function
[A] f(x) = ln x
[B] f(x) = ex-1
[C] f(x) = ln(x - 1)
[D] f(x) = ex

5. Review Problems
Sketch the graph: f(x) = ln|x|.

6. Review Problems
Solve for x: ln(5x + 1) + ln x = ln 4

7. Review Problems
Solve for x: ln(5x - 1) - ln x = 3.

8. Review Problems
dy/dx for y = ln(5 - x)6

9. Review Problems
Find the derivative: f(x) = ln(x3 + 3x)3

10. Review Problems
Find the derivative:

11. Review Problems
Find the derivative:

12. Review Problems
Find the derivative:

13. Review Problems
Differentiate: y = ln(ln tan x)

14. Review Problems
Find y’ y = ln|2x2 - 5|

15. Review Problems
Find y’ if ln xy = x + y

16. Review Problems
Use logarithmic differentiation to find

17. Review Problems
Find the slope of the tangent line to the graph of y = ln x2 at the point where x = e2

18. Review Problems
Evaluate the integral:
ln 4

19. Review Problems
Evaluate the integral:
ln|ax + b| + C

20. Review Problems
Evaluate the integral: -2

21. Review Problems
Evaluate the integral:

22. Review Problems Evaluate the integral: x + ln(x2 + 1) + C x +

23. Review Problems
Evaluate the integral:
8x + ln(x2 + 1) + C

24. Review Problems
Evaluate the integral:
9x ln(x2 + 1) + C

25. Review Problems
Evaluate the integral:
+ C

26. Review Problems
ln|sec 3x| + C
Evaluate the integral:
ln|sec 3x| + C

27. Review Problems Evaluate the integral:
-2 cos x + ln|csc x + cot x| + C

28. Review Problems
Evaluate the integral:
ln|tan x| + C

29. Review Problems
Evaluate the integral:

30. Review Problems Match the graph shown with the correct function
[A] f(x) = e (x-1)
[B] f(x) = e-(x-1)
[C] f(x) = ex + 1
[D] f(x) = e-x + 1

31. Review Problems
Differentiate:

32. Review Problems
Differentiate:

33. Review Problems
Differentiate:

34. Review Problems
Find: if xey + 1 = xy

35. Review Problems
Find the slope of the tangent line to the graph of y = (ln x)ex at the point where x = 2

36. Review Problems
Evaluate the integral:
-ecosx + C

37. Review Problems
Evaluate the integral:
+ C

38. Review Problems
Evaluate the integral:
-95 e-t/5 + C

39. Review Problems
Evaluate the integral:
+ C

40. Review Problems
Find if y = 3xx3
3xx2[3 + (ln 3)x]

41. Review Problems
Differentiate: y = x1-x
x1-x

42. Review Problems
Differentiate y = xx
xx[1 + ln x]

43. Review Problems
Evaluate the integral:
+ C

44. Review Problems
Find the area bounded by the function f(x) = 2-x, the x-axis, x = -2, and x = 1

45. Review Problems
A certain type of bacteria increases continuously at a rate proportional to the number present. If there are 500 present at a given time and 1000 present 2 hours later, how many will there be 5 hours from the initial time given?
2828

46. Review Problems
A certain type of bacteria increases continuously at a rate proportional to the number present. If there are 500 present at a given time and 1000 present 2 hours later, how many hours (from the initial given time) will it take for the numbers to be 2500? Round your answer to 2 decimal places.
4.64

47. Review Problems
A mold culture doubles its mass every three days. Find the growth model for a plate seeded with 1.6 grams of mold. [Hint: Use the model y = Cekt where t is time in days and y is grams of mold.]
1.6e t

48. Review Problems
The balance in an account triples in 21 years. Assuming that interest is compounded continuously, what is the annual percentage rate?
5.23%

49. Review Problems
The balance in an account triples in 20 years. Assuming that interest is compounded continuously, what is the annual percentage rate?
5.49%

50. Review Problems
A radioactive element has a half-life of 50 days. What percentage of the original sample is left after 85 days?
30.78%

51. Review Problems
A radioactive element has a half-life of 40 days. What percentage of the original sample is left after 48 days?
43.53%

52. Review Problems y = 10eln(12/5)t/6
The number of fruit flies increases according to the law of exponential growth. If initially there are 10 fruit flies and after 6 hours there are 24, find the number of fruit flies after t hours.
y = 10eln(12/5)t/6

53. Determine whether the function y = 2cos x is a solution to the differential equation
Review Problems
Determine whether the function y = 2cos x is a solution to the differential equation No

54. Review Problems verify that is a solution to the differential equation

55. Review Problems Find the particular solution to the differential
equation given the general solution
and the initial condition
y = 1 - cos x

56. Review Problems
Find the particular solution to the differential equation
given the general solution
and the initial condition y(0) = 5.

57. Review Problems
Use integration to find a general solution to the differential equation
y = (x + 1)3/ C

58. Review Problems
Use integration to find a general solution to the differential equation
y = 3 ln|1 + x| + C

59. Review Problems
Use integration to find a general solution to the differential equation y=

60. Review Problems
Find the general solution to the first-order differential equation: (4 - x)dy + 2y dx = 0
y = C(4 - x)2

61. Review Problems
Find the general solution to the first-order differential equation: x cos2y + tan y = 0
x2 + sec2y = C

62. Review Problems
Find the general solution to the first-order differential equation: y dx + (y - x)dy = 0
y ln|y| + x = Cy

63. Review Problems
Find the general solution to the first-order differential equation: y=

64. Review Problems
Find the general solution to the first-order differential equation:

65. Review Problems
Find the particular solution of the differential equation
that satisfies the initial condition y(0) = 7
y = e-x

66. Review Problems Find the solution to the initial value problem
y(-1) = 0
ey + sin y = (x2 + 1)

67. Review Problems Find the solution to the initial value problem
y(1) = 0
ln(1 + y2) = 2 ln x + x2 - 1