Mathematics 2121-01
Calculus for Life Sciences I
Fall 02
Dr. A. Shlapentokh
Test #2

1. Compute .
(a) 3/2
(b) 0
(c)
(d)
(e) None of the above
2. Compute .
(a) 3/2
(b) 0
(c)
(d)
(e) None of the above
3. Compute .
(a) 3/2
(b) 0
(c)
(d) 2/3
(e) None of the above
4. Compute .
(a) 0
(b)
(c) 1/2
(d)
(e) None of the above
5. Compute .
(a) -1/2
(b)
(c) 1/2
(d)
(e) None of the above
6. Let . What is the average rate of change of between and for any ?
(a) 1
(b) 2
(c) 3
(d) 1/2
(e) None of the above
7. Find the increment of the function in the interval .
(a) 4
(b) 3
(c) 2
(d) 1
(e) None of the above
8. Let . Let . Find the corresponding .
(a) -25
(b) 25
(c) -27
(d) 27
(e) None of the above
9. Find the average rate of change for the function in the interval .
(a) 1/5
(b) 1/6
(c) 1/3
(d) 1/4
(e) None of the above
10. Let . Find the average rate of change of in the interval .
(a)
(b)
(c)
(d)
(e) None of the above
11. Let . Find .
(a)
(b)
(c)
(d)
(e) None of the above
12. A population of harmful insects is growing according to the formula , where is measured in days and is measured in thousands of insects. Find the average rate of growth of the population of insects between t=1 and t=3 days.
(a) 9,000 insects
(b) 9 thousand insects/day
(c) 10 insects/day
(d) 10,000 insects
(e) None of the above
13. Compute .
(a)
(b) 0
(c) -1
(d) 1
(e) None of the above
14. Compute .
(a) 0
(b)
(c) 2
(d) 1
(e) None of the above
15. Compute .
(a)
(b)
(c)
(d)
(e) None of the above
16. Let . Compute .
(a)
(b)
(c)
(d)
(e) None of the above
17. Let . Compute .
(a)
(b)
(c)
(d) 1
(e) None of the above
18. Let . Compute .
(a) 2a
(b) a
(c) 3
(d) 1
(e) None of the above
19. Let Is continuous at ?
(a) This function is continuous at .
(b) The function is not continuous at because the function is not defined at .
(c) The function is not continuous at because does not exist.
(d) The function is not continuous at because .
(e) None of the above
20. Let Is continuous at ?
(a) The function is not continuous at because is not defined.
(b) The function is continuous at .
(c) The function is not continuous at because does not exist.
(d) The function is not continuous at because .
(e) None of the above
21. Let when and for some real number . Is there a value of that will make this function continuous at ?
(a) will make the function continuous.
(b) will make the function continuous.
(c) There is no that will make this function continuous because does not exist.
(d) will make the function continuous.
(e) None of the above.
22. Let , for and for some real number . Is there a value of that will make this function continuous at ?
(a) will make the function continuous.
(b) will make the function continuous.
(c) There is no that will make this function continuous because does not exist.
(d) will make the function continuous.
(e) None of the above.
23. Is the function continuous at ?
(a) The function is not continuous at because is not defined.
(b) The function is continuous at .
(c) The function is not continuous at because does not exist.
(d) The function is not continuous at because .
(e) None of the above
24. Let be a function differentiable everywhere. Then for what does the following equality always hold?
(a) 12
(b) 11
(c) 13
(d) 15
(e) None of the above
25. Let be a function differentiable everywhere. Then for what does the following equality always hold?
(a) 2
(b) 1
(c) 0
(d) -1
(e) None of the above
26. Let . The is equal to
(a) .
(b) .
(c) .
(d) .
(e) None of the above.
27. What is the slope of the tangent line to the graph of the function at ?
(a) 3/5
(b) 5/3
(c) 1
(d) 0
(e) None of the above.
28. What is the equation of the tangent line to the graph of at ?
(a)
(b)
(c)
(d)
(e) None of the above.
29. Suppose the amount of a drug in the blood of a patient is described by the formula , where is measured in minutes and is measured in mg. Find the instantaneous rate of growth of the amount of the chemical at .
(a) 17 mg
(b) 17 mg/minute
(c) 15 mg
(d) 15 mg/minute
(e) None of the above.
30. Find the derivative of .
(a)
(b)
(c)
(d)
(e) None of the above
31. Find the derivative of .
(a)
(b)
(c)
(d)
(e) None of the above
32. Find the derivative of .
(a)
(b)
(c)
(d)
(e) None of the above
33. Find the derivative of .
(a) 5
(b) 0
(c) 1
(d)
(e) None of the above
34. Find the derivative of .
(a)
(b) 11
(c) 1
(d) 0
(e) None of the above
35. Suppose , . Then
(a) cannot be determined from these data.
(b) =3
(c) =2
(d) does not exist.
(e) None of the above
36. Suppose , . Then
(a) cannot be determined from these data.
(b) =3.
(c) =2.
(d) does not exist.
(e) None of the above
37. Suppose , . Then
(a) cannot be determined from these data.
(b) =3.
(c) =2.
(d) does not exist.
(e) None of the above
Key
1(c), 2(a), 3(b), 4(c), 5(a), 6(b), 7(a), 8(c), 9(b), 10(a), 11(c), 12(b), 13(c), 14(a), 15(b), 16(a), 17(b), 18(d), 19(d), 20(b), 21(c), 22(c), 23(b), 24(b), 25(c), 26(b), 27(d), 28(e), 29(b), 30(c), 31(c), 32(e), 33(b), 34(b), 35(b), 36(b), 37(e)