Download Calculus Problem Solving Session: Distance, Limits, Fuel Efficiency, and Function Graphing and more Exams Calculus in PDF only on Docsity!
NAME_______________________________________
I______II______III______IV______V______VI______VII______ TOTAL ___________
September 26 Mathematics 105d Mr. Haines
2003 Calculus I
(10) I. The distance, s , a car has traveled on a trip is shown in the table as a function of the time,
t , since the trip started.
t (hours) 0 2 4 6 8 10 12
s (km) 0 3 12 27 48 75 95
A) Find the average velocity of the car between t = 2 hours and t = 10 hours.
B) Estimate the velocity of the car at t = 5 hours.
(20) II. Evaluate the limits if they exist. If they do not exist, explain why not:
A.
h
h
h
lim
2
0
โ
B.
2 3
3
lim x x
x
x (^) +
โโ
C.
h
h
h
lim โ 0 +
D.
h
h
h 0
lim โ
(10) V. Sketch below a graph of a function f with the following properties:
The domain of f is [-5, 5].
f ' is negative between โ3 and 3.
f is concave down on the interval [-5. 0].
f '' is nonnegative on the interval [0, 5].
f increases on the intervals [-5, -3] and [3, 5].
f '(-3) = f '(3) = 0.
(10) VI. Sketch below a graph of a function f with the following properties:
The domain of f is [-2, 2].
f is continuous at x = 1 , but f is not differentiable at x = 1.
f is not continuous at x = 0.
C)
3 / 4 7 2 t
t โ
D)
x
x
e
1 โ 3 e
