MAT 251: Sample Test #1
I. Multiple Choice
1. Compute the limit. lim
→ A. -5
C. −
B. 0
D. Does not exist
E. None of these
The following information is used in questions 2 and 3:
A balloon is blowing in the wind. Starting at noon, its height above the ground, measured in feet, can be
described by the function ℎ() = − + 1, where t is time in seconds past noon.
2. What is the balloon's average velocity for t between 0 and 4 seconds, that is, for the interval [0,4]?
A. 3 ft/sec
B. 4 ft/sec
C. 5 ft/sec
D. 6 ft/sec
E. None of these
D. 7 ft/sec
E. None of these
3. What was the balloon's velocity at the instant t = 3?
A. 4 ft/sec
B. 5 ft/sec
C. 6 ft/sec
()()
4. For the function () = , simplify the difference quotient:
A. −
B.
()
5. For the function () =
A. ′′() =
C. ′′() =
!
E. None of these
C.
D.
()
, find ′′().
B. ′′() =
D. ′′() = 0
()
.
E. None of these
MAT 251: Sample Test #1
$ $
6. Compute the limit: lim %
→ A.
B. −6
C.
D. 9
'
E. None of these
Use the following graph of y = g(x) to answer questions 7-10.
7. What is (−2)?
A. -3
B. 0
C. 1
D. 5
E. Does not exist
C. 1
D. 5
E. Does not exist
C. 1
D. 5
E. Does not exist
C. 1
D. 5
E. Does not exist
8. What is lim )()?
→
A. -3
B. 0
9. What is lim *()?
→
A. -3
B. 0
10. What is lim ()?
→
A. -3
B. 0
MAT 251: Sample Test #1
II. Free-response
11. Write an equation for the line tangent to () = √5 + 11at the point where x = 1.
12. An epidemic of influenza was declared in Arizona on December 31, 2012. The total number of cases
!
reported by day x of the outbreak can be described by the function -() = 200 √ + 100, where x indicates
st
the number of days since Dec 31 , 2012, so x = 1 is Jan 1 2013, x = 2 is Jan 2 2013, and so forth.
(a) What was the total number of reported influenza cases by Jan 10, 2013?
(b) At what rate was the number of cases of influenza growing on Jan 16, 2013?
13. () = 6 sin(). Find ′().
14. () = 0cos(). Find ′().
15. 3 =
.
Find
45
∣
.
4 7
Use the following information to answer questions 16-18:
9
The body temperature, T, of a person during an illness is given by 8() = 9 + 98.6. T is measured in degrees
Fahrenheit and time, t, in hours since the illness was acquired.
16. Find the average rate of body temperature change in degrees per hour, for the first 2 hours, that is, for t in
the interval[0,2].
17. Find the body temperature at t = 2.
18. Find the rate of body temperature change in degrees per hour at 2 hours into the illness, that is, at t = 2.