Math 460 Problem set 1
Due 1/21/10
Problem 1 p. 25 Exercises 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 0.9
Problem 2 Each of the following is of one of these types: number, set, string.
Identify the type of each. Assume = cfw_a, b, c.
zero
cfw_
ababb
cfw_
Angular Kinetics
Parameters
Torque
Definition
Units
Couple
Center of Gravity (Mass)
Moment of Inertia
Steiners Theorem or Parallel Axis Theorem
Angular Momentum (H)
Newtons First Angular Law
The Law of Inertia
In the absence of an external torque exerted
Math 210 Make-up Midterm 1 answers
Problem 1 (5 pts) If f (2) = 5 and f (2) = 9, nd the formula for the tangent line to f (x) at x = 2.
The slope is 9 and the point is (2, 5). Using the point-slope equation for a line, we have
y = 5 + 9(x 2)
Problem 2 (5
Math 210 Midterm 1 answers
Problem 1 (5 pts) Find the domain of
f (x) =
x 1 + ln(2 x).
For x 1 to be dened, we must have x 1 0, which is the same as x 1. For ln(2 x) to be
dened, we must have 2 x > 0, which is the same as x < 2. Therefore, for f (x) to be
Math 210 Midterm 2 Answers
Problem 1 (5 pts) Find the derivative:
f (x) = x5 + 10x3 + 5x + 8
f (x) = 5x4 + 10 3x2 + 5
Problem 2 (5 pts) Find the derivative:
g(t) = 10e8t
Constant multiple rule and chain rule.
g (t) = 10e8t 8
Problem 3 (5 pts) Find the der
Math 210 Midterm 3 Answers
Problem 1 (10 pts) Find where the following function is decreasing.
f (x) = x3 + 15x2 600x + 50
We take the rst derivative:
f (x) = 3x2 + 30x 600
To nd its critical points, we set this equal to zero:
3x2 + 30x 600 = 0
and solve:
Math 104 Midterm 3 Answers
Problem 1 (5 pts) Solve for x in degrees (to the nearest degree), if we assume x is between 0 and 90 .
7 sin x + 1 = 4
7 sin x + 1 =
4
7 sin x =
3
3
7
sin x =
x =
sin1
x =
3
7
25
Problem 2 (10 pts) Solve for x in degrees. Find a
Math 104 Midterm 2 answers
Problem 1 (5 pts) Sketch the graph of y = sin(x) + 1 in the graph given below.
We establish the period as (2)/() = 2. Other than that the graph is shifted up by 1. Note in this and
other graphs that you were supposed to graph th
Math 104 Midterm 1 Answers
Problem 1 (5 pts) Identify the following angles as acute, right, obtuse, or straight:
39 : acute
92 5 : obtuse
130 : acute (note: 130 minutes is a little more than 2 degrees)
/2 radians: right
180 : straight
Problem 2 (5 pt
Linear Kinetics
Parameters
Force
Definition Units
Inertia
Mass Weight
System
Types of Forces
Internal External
Linear Momentum (p)
Sir Isaac Newton
1643 - 1727 "Principia Mathematica Philosophiae Naturalis" in 1686. More here.
Newtons Law of Gravitiation