| 1. |
Simplify  .
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| 2. |
Simplify  .
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| 3. |
Express the following in scientific notations:  .
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| 4. |
Express the following in scientific notations:  .
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| 5. |
Express the following in scientific notations:  .
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| 6. |
Compute:  .
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| 7. |
Compute:  .
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| 8. |
Compute:  .
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| 9. |
Solve:  .
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| 10. |
Solve:  .
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| 11. |
Suppose  and  are related by the formula  , where  and  . What is the relationship between  and  ?
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| 12. |
Suppose  and  are related by the formula  , where  . What is the relationship between  and  ?
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| 13. |
Compute the derivative:  .
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| 14. |
Compute the derivative:  .
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| 15. |
Compute the derivative:  .
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| 16. |
Compute the derivative:  .
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| 17. |
Compute the derivative:  .
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| 18. |
Compute the derivative:  .
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| 19. |
Compute the derivative:  .
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| 20. |
Compute the third derivative of  .
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| 21. |
Compute the derivative:  .
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| 22. |
Compute the derivative:  .
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| 23. |
Compute the derivative:  .
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| 24. |
Compute the derivative:  .
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| 25. |
Compute the derivative:  .
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| 26. |
Compute the third derivative of  .
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| 27. |
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?
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| 28. |
Consider the same population as in the problem above but use once a year compunding. (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.
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| 29. |
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?
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| 30. |
Find two positive numbers whose sum is 10 and the sum of their cubes is as small as possible.
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| 31. |
A farmer is making a rectangular yard using 300 ft of fencing. How big can the area of the yard be ?
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| 32. |
Find the largest value of the function  in the interval  .
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| 33. |
Find the absolute minimum and maximum values of  in the interval  .
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| 34. |
Determine the minimum value of the function  in the interval  .
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| 35. |
Determine the maximum value of the function  in the interval  .
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| 36. |
Determine the minimum value of the function  in the interval  .
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| 37. |
Determine the minimum value of the function  in the interval  .
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| 38. |
Determine the minimum value of the function  in the interval  .
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| 39. |
Find all the critical points of the function  and determine their nature.
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| 40. |
Find all the critical points of the function  and determine their nature.
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| 41. |
Find all the critical points and determine their nature for the function  .
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| 42. |
Determine for what values of  the function  concaves up.
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| 43. |
Find all the inflection points of the function  .
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| 44. |
For what values of  is the function  increasing ?
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| 45. |
For what values of  is the function  decreasing ?
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| 46. |
For what values of  is the function  decreasing ?
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| 47. |
For what values of  is the function  increasing ?
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| 48. |
Amongst the graphs below which graph(s) has (have) an inflection point ?
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| 49. |
Amongst the graphs above which graph(s) has (have) a critical point ?
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| 50. |
Amongst the graphs below which one corresponds to the function  with  and  ?
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| 51. |
Amongst the graphs below which one corresponds to the function  with  and  ?
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| 52. |
Amongst the graphs below which one corresponds to the function  with  and  ?
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| 53. |
Amongst the graphs below which one corresponds to the function  with  and  ?
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