Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Section 10.1: Solutions of Dierential Equations
An (ordinary) dierential equation is an equation involving a function and its derivatives. That is, for functions P (x0 , x1 , . . . , xn ) and Q(x0 , . . . , xn ) of n + 1 variables, we say that the functio
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Math 126
Final Review
1. Evaluate the following integrals: (a)
Z
1
x sin(x/2) dx
2
(b)
2. Find the area of the region bounded by the curves y = x3
Z
1
x2
1
2x and y = x2 .
p
1
x3 dx
3. Evaluate each integral. Clearly identify any substitutions used.
Z
(a)
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Math 126
Binomial Random Variables
Suppose an experiment has exactly two possible outcomes: success or failure. And further suppose the
following:
The experiment is repeated several times in a row (each time is called a trial);
Each trial has the same t
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
MATH 126
An Assortment of Topics?
1. Determine the value of A so that f (x) is a probability density function on the given interval.
(a) f (x) = A(15
(b) f (x) = Ae
6x
3x) for 1 x 4 (and zero otherwise. . . )
for x
(c) f (x) = Ax4 (1
0 (and zero otherwise
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Solutions to Exercises on Newtons Law of Cooling
S. F. Ellermeyer
1. A thermometer is taken from a room that is 20 C to the outdoors where
the temperature is 5 C. After one minute, the thermometer reads 12 C.
Use Newtons Law of Cooling to answer the follo
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Taylor Polynomials and Series
Probability
Term
random variable
expected value
(or mean)
standard
deviation
Definition
Application
continuous:
=E ( X )= X F PDF ( X) dX
( X ) = V ( X )
1
CRV = (a+ b)
2
1
( X CRV )=
(ba)
12
V ( X )= ( X )2 F PDF ( X ) dX
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Seminole State Homepage


Calculus I
Calculus II
Calculus Homepage
ExamplesApplication Problems
Example 15: Exponential Population Growth Example
Exponential Population Growth
The population of a country is growing at a rate that
is proportional to the
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
NEWTONS LAW OF COOLING OR HEATING
Let
T = temperature of an object,
M = temperature of its surroundings, and
t = time.
If the rate of change of the temperature T of the object is directly proportional to the
difference in temperature between the object an
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Sig Fig and Dimensional analysis practice problems
Evaluate each of the following and write the answer to the appropriate number of significant figures.
a. 212.2 + 26.7 + 402.09=641.0
b. 1.0028 + 0.221 + 0.10337=1.327
c. 52.331 + 26.01  0.9981=77.34
d. 0