Mathematics 2122-001
Calculus for Life Sciences II
Fall 2004
Test #2
Instructor: Dr. Alexandra Shlapentokh
1.
(a) 0
(b) 1
(c) 2
(d) 3
(e) None of the above
2. Suppose . Then what is ?
(a)
(b)
(c)
(d)
(e) None of the above
3. Suppose . Then what is ?
(a)
(b)
(c)
(d)
(e) None of the above
4. Suppose and . Then is equal
(a) 1
(b) -1
(c) 0
(d) 2
(e) None of the above
5. Find the area under and above between and .
(a)
(b)
(c)
(d)
(e) None of the above
6. Find the area bounded by .
(a)
(b)
(c)
(d)
(e) None of the above
7. The area bounded by the curves and .
(a) 1000
(b) 2000
(c) 3000
(d) 4000
(e) None of the above
8. Consider a function with the following graph.

The area bounded by the graph of , lines , and is equal to
(a)
(b)
(c)
(d)
(e) None of the above
9. Consider the two graphs below intersecting at the point . What is the area bounded by the two graphs and the lines ?

(a)
(b)
(c)
(d)
(e) None of the above
10. This question refers to the same graphs as Question 9. What is the area bounded by the two graphs, and the line ?
(a)
(b)
(c)
(d)
(e) None of the above
Hint: the range for is .
11. Suppose you have to compute the area bounded by two everywhere continuous graphs , and lines , . Assume further that for we have that . Then the area in question is equal to
(a)
(b)
(c)
(d)
(e) None of the above
12. Suppose you have to compute the area bounded by two everywhere continuous graphs , and lines , . Assume further that for we have that , and for we have that . Then the area in question is equal to
(a)
(b)
(c)
(d)
(e) None of the above
13. Suppose is a function continuous everywhere with for , for . Then the area bounded by the graph of , lines is equal
(a)
(b)
(c)
(d)
(e) None of the above
14. Suppose an antiderivative of is . Then
(a) cannot be determined.
(b) is .
(c) is .
(d) is .
(e) None of the above
15. Suppose has an antiderivative . Then
(a) has no other antiderivatives.
(b) has infinitely many antiderivatives.
(c) has one more antiderivative.
(d) has two more antiderivatives.
(e) None of the above
16. Let and be antiderivatives of the same function. Then
(a) is a constant.
(b) is equal to .
(c) is equal to .
(d) is equal to .
(e) None of the above
17. Suppose , where is a constant. Then any antiderivative of is of the form
(a) , where is a constant.
(b) .
(c) , where is a constant.
(d) , where is a constant.
(e) None of the above
18. Suppose , where is a constant. Then any antiderivative of is of the form
(a) , where is a constant.
(b) , where is a constant.
(c) .
(d) , where is a constant.
(e) None of the above
In Problems 19–32 let be an antiderivative of the given function. Determine .
19.
(a) 7
(b) -7
(c) 0
(d) 1
(e) None of the above
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. Let . Then
(a) is
(b) is
(c) cannot be determined from these data
(d) does not exist
(e) None of the above
37. Let . Then
(a) is .
(b) is .
(c) cannot be determined from these data
(d) does not exist
(e) None of the above
Key
1(a), 2(b), 3(c), 4(c), 5(c), 6(b), 7(d), 8(d), 9(d), 10(a), 11(a), 12(d), 13(c), 14(d), 15(b), 16(a), 17(c), 18(b), 19(b), 20(e), 21(a), 22(c), 23(c), 24(b), 25(a), 26(e), 27(e), 28(a), 29(a), 30(a), 31(b), 32(d), 33(b), 34(b), 35(a), 36(b), 37(b)





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