| 1. |
Differentiate  .
 |
| 2. |
Differentiate, using the product rule,  .
|
| 3. |
Suppose  , where  . Compute  .
|
| 4. |
Using the same information as in the preceding problem, compute  , where  .
|
| 5. |
Compute the derivative:  .
|
| 6. |
Compute the derivative:  .
|
| 7. |
Compute the derivative:  .
|
| 8. |
Compute the derivative:  .
|
| 9. |
Compute the derivative:  .
|
| 10. |
Compute the derivative:  .
|
| 11. |
Suppose  and  are functions defined and differentiable everywhere. Suppose  . What is  ?
|
| 12. |
Compute the third derivative of  .
|
| 13. |
Compute the second derivative of  .
|
| 14. |
Simplify  .
|
| 15. |
Simplify  .
|
| 16. |
Express the following in scientific notations:  .
|
| 17. |
Express the following in scientific notations:  .
|
| 18. |
Express the following in scientific notations:  .
|
| 19. |
Compute:  .
|
| 20. |
Compute:  .
|
| 21. |
Compute:  .
|
| 22. |
Solve:  .
|
| 23. |
Solve:  .
|
| 24. |
Suppose  and  are related by the formula  , where  and  . What is the relationship between  and  ?
|
| 25. |
Suppose  and  are related by the formula  , where  . What is the relationship between  and ?
|
| 26. |
Compute the derivative:  .
|
| 27. |
Compute the derivative:  .
|
| 28. |
Compute the derivative:  .
|
| 29. |
Compute the derivative:  .
|
| 30. |
Compute the derivative:  .
|
| 31. |
Compute the derivative:  .
|
| 32. |
Compute the derivative:  .
|
| 33. |
Compute the third derivative of  .
|
| 34. |
Compute the derivative:  .
|
| 35. |
Compute the derivative:  .
|
| 36. |
Compute the derivative:  .
|
| 37. |
Compute the derivative:  .
|
| 38. |
Compute the derivative:  .
|
| 39. |
Compute the third derivative of  .
|
| 40. |
A certain population is growing at the uniform rate of 3% when time is measured in years (with the growth rate always proportional to the population size). In 1998 the population was 500. What will it be in 2005?
|
| 41. |
Consider the same population as in the problem above but use a discrete model. (In other words the population increase is computed once a year using a 3% rate.) Assume again that the population size was 500 in 1998 and determine the population in 2005.
|
| 42. |
Suppose a certain radioactive element is decaying exponentially with a half time equal to 1000 years. How long will it take for 75% of the original amount to be lost?
|
