Population parameters or population characteristics can be estimated by taking representative samples of a population. In other words, conclusions about an entire population can be inferred from a sampling of that population. This sampling of the population can then be examined and inferences made about the general population it represents. Various measures provide different types of data or measures of data from which conclusions can be derived. Examples of these types of measures are Measures of Central Tendency and Measures of Dispersion.
Address all of the following questions in a brief but thorough manner.

• What are the most common measures of central tendency? Include brief definitions for the common measures of central tendency as part of your initial posting.
• How do these measures differ? How are they the same?
• What information is provided by each of these measures and what do they tell us? How could you use measures of central tendency in decision making as a leader and/or manager?
• What are the various measures of dispersion?
• What are the uses of these measures and what are their limitations?
• What does each of these measures tell a researcher? A leader or manager?

The final paragraph (three or four sentences) of your initial post should summarize the one or two key points that you are making in your initial response.

AMERICAN UNIVERSITY OF THE MIDDLE EAST
MA166 – Analytic Geometry and Calculus II, Fall 2020, Section: O2
Assignment 3, Due: Dec 8
th
Instructions: There are 4 questions. Please answer clearly, show all your work step by step.
Student Name/ID: ___________________________________________________________
Student Name/ID: ___________________________________________________________
Q1 [25 pts]: Justify your answers clearly.
a) [8 pts] Evaluate the integral ∫
(𝑥−3)
(𝑥−4)(𝑥+5)
𝑑𝑥
 
b) [10 pts] First use a substitution and then partial fractions to evaluate the integral ∫
𝑑𝑥
 
 
1
𝑥√𝑥+1
c) [7 pts] When we calculate the integral of a rational function by partial fractions, in which
case(s) we get an inverse tangent function in the end? Explain your answer.
Q2 [25 pts]: Justify your answers clearly.
a) [10 pts] Evaluate the integral ∫ 𝑒
−4𝑥
𝑑𝑥
1
−∞
or show that it is divergent.
 
 
 
 
b) [8 pts] Evaluate the integral ∫
1
𝑑𝑥
1−𝑥
or show that it is divergent.
 
 
 
 
c) [7 pts] What is an improper integral of Type I? Give an example and explain why it is improper
of Type I.
 
Q3 [25 pts]: Justify your answers clearly.
a) [10 pts] Sketch the region enclosed by the curves 𝑦 = 𝑥, 𝑦 = 1/𝑥
, and the line 𝑥 = 2 and
find its area.
2
 
 
 
b) [8 pts] Find the area between the curves 𝑦 = 𝑥
and 𝑦 = 3𝑥.
 
 
 
2
c) [7 pts] Does the integral ∫ (𝑥 − 𝑥
2
)𝑑𝑥
1
represent the area of a region? If so, make a sketch of
the region.
Q4 [25 pts]: Justify your answers clearly.
a) [10 pts] Find the volume of the solid generated by revolving the region bounded by 𝑦 = √𝑥,
𝑦 = 2, and 𝑥 = 0 about the 𝑥-axis.
 
 
 
b) [8 pts] Find the volume of the solid generated by revolving about the 𝑥-axis the region
bounded by 𝑦 = 4 − 𝑥
and the 𝑥-axis.
 
 
2
c) [7 pts] A region between two curves (where 𝑥 ≥ 0) is rotated about the 𝑥-axis. The crosssections
of
the
resulting
object
are
as
follows.
Draw
the
region
that
is
rotated
and
write
the
integral
which
gives
the
volume.