Math 141
Name:
Homework 4
1. In the theory of electrical circuits, Ohms law describes the relationship between the voltage V across
a resistor, the electrical current I passing through the resistor, and a quantity R known as the resistance.
The law can be
Math 141
Name:
Homework 5
1. When expanding adiabatically (i.e. without gaining or losing heat), the pressure P and volume V of a
sample of argon gas are related by the formula
PV 5/3 = constant.
(a) Take the derivative of the above equation to nd a formu
Math 141
Name:
Homework 7
1. Little Joey is riding the Ferris wheel at the county fair:
The wheel has a radius of 40 feet, and the center of the wheel sits 45 feet above the ground. Let h be
little Joeys height above the ground, and let be the angle shown
Math 141
Name:
Homework 2
1. (a) Use a straightedge to draw tangent lines to the following graph at x = 3, 2, 1, 0, 1, 2, and 3.
4
y
3
2
1
0
x
3
2
1
(b) Use your tangent lines to estimate the values of
table showing your answers.
0
1
2
3
dy
for x = 3, 2,
Math 141
Name:
Homework 1
1. At age 3, little Joey was 3 feet tall. By age 5, he had grown to 3 feet, 5 inches.
(a) Assuming linear growth, how tall do you expect Joey to be at age 8?
(b) Write an approximate linear formula for Joeys expected height at ag
Math 141
Name:
Homework 6
1. A man with a video camera is standing 4000 ft. from the base of a rocket launching pad, recording the
launch:
2
)
4000 ft.
Because the rocket is ascending, the man must constantly adjust the angle of the camera to match the
an
Math 141
Name:
Homework 3
1. Consider the following formula for the area of an isosceles triangle:
a
a
Area =
1 2
a sin
2
(a) A unit pentagon is a regular pentagon with a radius of 1, as shown in the following gure. Use the
area formula above to nd the a
Practice Problem Solutions: Exam 1
1. (a) Plugging in 10, 100, and 1000 for x gives 0.333148, 0.333331, and 0.333333, respectively. Thus,
the limit is 1/3 .
(b) Plugging in 100, 1000, and 10,000 for x gives 1.10526, 1.01005, and 1.00100, respectively.
Thu
Math 141
Name:
Quiz 4
1. [20 points (5 pts each)] Find a formula for
(a) P =
R
Q+
3
(b) P = 1 Q 2
2
5
dQ
dR
dP
in terms of Q, R,
, and
.
dt
dt
dt
(c) P = Q 2 R
(d) P = Q(1 + 4R)3
Math 141
Name:
Homework 9
1. A freight company wants to manufacture large metal shipping containers. The containers will have the
shape of a box with no top, and must be twice as long as they are wide:
2
B
#B
Material for the bottoms of the containers cos
Math 141
Name:
Exam 1
1. [12 points (6 pts each)] Evaluate each of the following limits.
(a) lim
x
x2
x 4x2
(3h + 2)2 4
(b) lim
h0
h
2. [12 points (6 pts each)] In the theory of electrical circuits, Joules law describes a relationship between the power P
Math 141
Name:
Quiz 3
1. [6 points (3 pts each)] Evaluate each of the following limits. You may use any method you like.
(a) lim
5x2
x3 + 4
(b) lim
x2
x2
x
x0
2. [4 points] Let f (x) = 3x . Write a limit for f (2). You do not need need to simplify your an
Math 141
Name:
Quiz 1
The Mauna Loa Observatory observatory in Hawaii regularly measures the concentration of CO2 in the
atmosphere. In the year 2000, the observatory measured 371 ppm (parts per million) of CO2 in the atmosphere; in 2010, the observatory
Math 141
Name:
Quiz 2
During a certain chemistry experiment, the mass of salt (NaCl) in grams decreases according to the formula
M =
9 1.5t ,
where t is the time in minutes.
(a) [1 point] How much salt is present at the beginning of the experiment?
dM
at