Mathematics 2171-01
Calculus I
Spring 04
Dr. A. Shlapentokh
Test #3

1. Compute the third derivative of
(a)
(b)
(c)
(d)
(e) None of the above
2. Suppose a rectangle has a constant area equal to 30 mm and one of the sides is equal to 10 mm while changing at the rate of 1 mm/sec. Find the rate of change for the second side.
(a) Cannot be determined from this information.
(b) 0.3 mm/sec
(c) -0.3 mm/sec
(d) 3 mm/sec
(e) None of the above
3. Find all the critical points of function .
(a) This function has no critical points.
(b)
(c) is any integer.
(d) is any integer.
(e) None of the above
4. Find all the critical points of the function .
(a) This function has no critical points.
(b) is the only critical point.
(c) is the only critical point.
(d) and are the only critical points.
(e) None of the above
5. Find all the critical points of the function .
(a) This function has no critical points.
(b) is the only critical point.
(c) is the only critical point.
(d) and are the only critical points.
(e) None of the above
6. Find all the local maxima and minima for the function :
(a) No local maxima or minima
(b) Local maximum at 0, local minimum at -4
(c) Local maximum at -4, local minimum at 0
(d) Local maximum at -4 and 0
(e) None of the above
7. Find for what values of the function is increasing.
(a) This function is always decreasing.
(b) This function is always increasing.
(c) This function is increasing for .
(d) This function is increasing for .
(e) None of the above
8. Find all the values of for which the function concaves up.
(a) The graph of this function always concaves up.
(b) The graph of this function always concaves down.
(c) The graph of this function concaves up for .
(d) The graph of this function concaves up for .
(e) None of the above
9. Which of the following statements is true?
(a) has a vertical asymptote .
(b) has a horizontal asymptote .
(c) has no asymptotes.
(d) has a slant asymptote .
(e) None of the above
10. Find the maximum value of the function in the interval .
(a) 20
(b)
(c)
(d)
(e) None of the above
11. Which of the following graphs is a graph of a function with and
(a)
(b)
(c)
(d)
(e) None of the above
12. Which of the graphs in Problem 11 is a graph of the function with and
13. Which of the graphs in Problem 11 is a graph of the function with and
14. Which of the graphs in Problem 11 is a graph of the function with and
15. Which of the graphs in Problem 11 has a critical point?
16. Let . Then, according to the Mean Value Theorem, there exists an such that
(a)
(b)
(c)
(d)
(e) None of the above
In Problems 17 – 24 compute the limits:
17.
(a)
(b)
(c)
(d)
(e) None of the above
18.
(a)
(b)
(c)
(d)
(e) None of the above
19.
(a)
(b)
(c)
(d)
(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)
(b)
(c)
(d)
(e) None of the above
24.
(a)
(b)
(c)
(d)
(e) None of the above
25. Find the point on the line which is the closest to the point .
(a) (1,1)
(b) (3,3)
(c) (5,5)
(d) (7,7)
(e) None of the above
Key
1(c), 2(c), 3(d), 4(b), 5(c), 6(a), 7(b), 8(d), 9(e), 10(b), 11(c), 12(a), 13(b), 14(d), 15(e), 16(c), 17(c), 18(c), 19(a), 20(b), 21(e), 22(c), 23(d), 24(e), 25(a)





Created by MicroPress TeXpider.