Worked problem in calculus. Given an initial investment of $1000 and a nominal annual interest rate of 5%, compute the amount accrued after 10 years by compounding annually, monthly, daily, and continuously. Find the time to double the initial investment if compounding is annual or continuous.

1. Definition of ln(x) Using Integration
2. Properties of ln(x) Using Integration
3. End Behavior of ln(x)
4. Derivative of ln(x) as a Slope
5. The Chain Rule for ln(x) and ln|x|
6. Derivative of f(x) = ln(ln(x^2 + 1))
7. Graph of f(x) = 3ln(x-2) + 4
8. Graph of f(x) = ln(x^2 - x)
9. Graph of f(x) = ln|x^2-x|
10. Implicit Differentiation with ln(x)
11. Logarithmic Differentiation
12. Antiderivative of ln(x^4)/x
13. Antiderivative involving 1/x 1
14. Antiderivative involving 1/x 2
15. Trig Antiderivatives involving 1/x
16. Area under f(x) = ln(x)/x
17. Inverse Functions
18. Inverse Functions: ln(x) and exp(x)
19. Graph of f(x) = 2 - e^{2x-1}
20. Inverse Function for f(x) = 2 e^{x-2}
21. No Inverse Function for f(x)=ln(x)-exp(x)
22. Derivative of an Inverse Function
23. Properties of Derivative of exp(x)
24. Derivatives with e^x
25. Tangent Line to x^2 e^x at x=1
26. Graph of f(x) = x^2 e^{-x}
27. Graph of Normal Distribution
28. Implicit Differentiation with e^x
29. Indefinite Integrals with e^x
30. Definite Integral of exp(-3x+2) (HD Version)
31. Definite Integral of (e^x - 1)(e^x - 2)/e^2x (HD Version)
32. Graphing with 2^x
33. Equations with Logarithms
34. Derivatives of log_b(x) and b^x
35. Tangent Lines to log_b(x) and b^x
36. Logarithmic Differentiation
37. Indefinite Integrals with b^x and log_b(x)
38. Definite Integrals with b^x and log_b(x)
39. Compound Interest
40. Evaluating Inverse Trig Functions 1
41. Evaluating Inverse Trig Expressions 2
42. Evaluating Inverse Trig Expressions 3
43. Derivatives of Inverse Trig Functions
44. Graph of f(x) = tan^{-1}(1-x^2)
45. Tangent Line to f(x) = xsin^{-1}(x/2)
46. Integrals with Inverse Trig Functions 1
47. Integrals with Inverse Trig Functions 2
48. Integrals with Inverse Trig Functions 3

In this third installment, Dr. Bob resumes his Calculus series by solving derivatives and definite integrals of special functions: Derivative of ln(x), Integration with ln(x), Inverse functions, Derivative and integral with e^x, Other Bases, Derivatives of Inverse Trig, Integrals of Inverse Trig.