Mathematics 2122-002
Calculus for Life Sciences II
Fall 2002
Test #2
Instructor: Dr. Alexandra Shlapentokh
In Problems 1 – 8 differentiate the given function with respect to x.
1. _
(a)
(b)
(c)
(d)
(e) None of the above
2.
(a)
(b)
(c)
(d)
(e) None of the above
3.
(a)
(b)
(c)
(d)
(e) None of the above
4.
(a)
(b)
(c)
(d)
(e) None of the above
5.
(a)
(b)
(c)
(d)
(e) None of the above
6.
(a)
(b)
(c)
(d)
(e) None of the above
7. .
(a)
(b)
(c)
(d)
(e) None of the above
8. _
(a) The derivative does not exist.
(b)
(c) The derivative cannot be determined from these data.
(d)
(e) None of the above
In Problems 9 – 13 determine the smallest period of the given function.
9. _
(a) This function is not periodic.
(b)
(c)
(d)
(e) None of the above
10.
(a) This function is not periodic.
(b)
(c)
(d)
(e) None of the above
11.
(a) This function is not periodic.
(b)
(c)
(d)
(e) None of the above
12.
(a) 1
(b) 2
(c)
(d)
(e) None of the above
13. _
(a)
(b)
(c)
(d)
(e) None of the above
In Problems 14 – 16 determine the amplitude of the given function.
14. _
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
15.
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
16. . _
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
17. A certain variable varies sinusoidally between -1 and 1 with a period of 1 day. The variable reaches its highest value at 3 pm each day. Find a formula for .
(a) , where is measured in hours and corresponds to 12 am.
(b) , where is measured in hours and corresponds to 12 am.
(c) , where is measured in hours and corresponds to 12 am.
(d) , where is measured in hours and corresponds to 12 am.
(e) None of the above
18. A certain variable varies sinusoidally between 2 and 6 with a period of 3 days. The variable reaches its highest value at 12 am of the second day. Find a formula for .
(a) , where is measured in days and corresponds to 12 am of the first day of the cycle.
(b) , where is measured in days and corresponds to 12 am of the first day of the cycle.
(c) , where is measured in days and corresponds to 12 am of the first day of the cycle.
(d) , where is measured in days and corresponds to 12 am of the first day of the cycle.
(e) None of the above
19. What is the degree of the trigonometric polynomial ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
In Problems 20 – 31 let be an antiderivative of the given function. Determine .


20.
(a)
(b)
(c)
(d)
(e) None of the above
21.
(a)
(b)
(c)
(d)
(e) None of the above
22.
(a)
(b)
(c)
(d)
(e) None of the above
23.
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
24.
(a)
(b)
(c)
(d)
(e) None of the above
25.
(a)
(b)
(c)
(d)
(e) None of the above
26.
(a)
(b)
(c)
(d)
(e) None of the above
27.
(a)
(b)
(c)
(d)
(e) None of the above
28.
(a)
(b)
(c)
(d)
(e) None of the above
29.
(a)
(b)
(c)
(d)
(e) None of the above
30.
(a)
(b)
(c)
(d)
(e) None of the above

31.
(a)
(b)
(c)
(d)
(e) None of the above
32.
(a)
(b)
(c)
(d)
(e) None of the above
In Problems 33 – 35 assume that and is a constant. Determine which statements below are always true under the given assumptions.
33. _
(a)
(b)
(c)
(d) does not exist
(e) None of the above
34.
(a)
(b)
(c)
(d) does not exist
(e) None of the above
35. _
(a)
(b)
(c)
(d) does not exist
(e) None of the above
36. Use the formula to compute .
(a)
(b)
(c)
(d)
(e) None of the above
37. .
(a) 0
(b) 1
(c) 2
(d) 3
(e) None of the above
38. Suppose . Then what is ?
(a)
(b)
(c)
(d)
(e) None of the above
39. Find the area under and above between and .
(a)
(b)
(c)
(d)
(e) None of the above
40. Find the area bounded by .
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above
41. The area bounded by the curves and .
(a) 500
(b) 1000/3
(c) 200
(d) 250
(e) None of the above
Key
1(b), 2(d), 3(a), 4(d), 5(d), 6(c), 7(b), 8(b), 9(c), 10(b), 11(c), 12(e), 13(c), 14(a),15(b), 16(e), 17(b), 18(d), 19(c), 20(d), 21(a), 22(c), 23 (b), 24(b), 25(c), 26(a), 27(b), 28(a), 29(a), 30(b), 31(a), 32(b), 33(a), 34(b), 35(a), 36(a), 37(a), 38(c), 39(a), 40(d), 41(b)