MTH 230 Project Problem 3 Name: _________________________ 1. Given  2 2),2sin(8),2cos(8)( ttttr , find A) the unit tangent vector B) The arclength on the interval [0,t]. C) The arclength on the interval [0, 2]. (Show all definitions and work.) 2. A) Use the formula 3 r rr    to find the curvature at t = 2  and at t =2. B) Find the radii of the osculating circles at t = 2  and at t =2. (Show all definitions and work.) 3. Use Mathematica to find the Unit Normal Vector for  2 2),2sin(8),2cos(8)( ttttr . 4. Use the results in problems 1. and 3. to find the Binormal Vector at t = 2  . (Show the definitions and work.) 5. Find the equation of the Normal Plane at t = 2  .(Show the definitions and work.) 6. Find the equation of the Osculating Plane at t = 2  . (Show the definitions and work.) 7. Given r(t) = ttt etete ,cos,sin find A) the unit tangent vector B) The arclength on the interval [0,t]. C) The arclength on the interval [0, ln4]. (Show all definitions and work.) 8. A) Reparameterize the curve in problem 7. according to arclength. B) Find the location when one has traveled a distance of ln2 from 0 on this curve. 9. Given r(t) = ttt etete ,cos,sin the Unit Normal Vector. (Show the definitions and work. This requires some patience, but does work out.) 10. Find the curvature at t = ln4 on the curve r(t) = ttt etete ,cos,sin . 11. Given a cycloid x = a(t – sint) and y = a( 1 – cost) which the path traced by a point on a rolling circle. The interval [0, 2] produces one arch of the cycloid. Show the work that proves that the arclength of one arch is 8a. 12. State the domain and ranges of  2 2),2sin(8),2cos(8)( ttttr . 13. State the domain and ranges of r(t) = 2 2 22 7 2 , , 8 88 t t t tt   . 14. Find the 2 2 22 7 2 lim , , 8 88 t t t t tt    . 15. Find the velocity, acceleration, and speed of a particle with the given position function. 2 ( ) 4 ,sin(2 ) 2 cos( ), cos(2 ) 2 sin( )r t t t t t t t t   16. Read the parametric equations for trajectory motion on page 889. A projectile is fired with an initial speed of 180 m/sec and angle of elevation 54º. A) Find the range of the projectile B) the maximum height reached and c) the speed at input. 17. Read page 890 and find the tangential and normal components of the acceleration vector. 2 ( ) , ,3r t t t t Running head: Stress In College Students 1 Stress In College Students 2 Stress in College Students (Drafted Version) Name Professor : Class Date: Stress in College Students The life of a college student is greatly marked with a high incidence of stress occurrence. However, not all college students suffer from stress. The stress response depends on personal readiness to cope with the demands of the situation and the situation itself to which one refers. That is, how an individual responds to stressful events depends o.

1. MTH 230 Project Problem 3 Name:
_________________________
2
2),2sin(8),2cos(8)( ttttr , find A) the unit tangent vector B) The
arclength on the
all definitions and work.)
2. A) Use the formula
3
r
rr
2

2. osculating circles at t =
2
2
2),2sin(8),2cos(8)( ttttr .
4. Use the results in problems 1. and 3. to find the Binormal
Vector at t =
2
. (Show the definitions and
work.)
5. Find the equation of the Normal Plane at t =
2
.(Show the definitions and work.)
6. Find the equation of the Osculating Plane at t =
2
. (Show the definitions and work.)
7. Given r(t) =

3. ttt
etete ,cos,sin find A) the unit tangent vector B) The arclength
on the interval [0,t].
C) The arclength on the interval [0, ln4]. (Show all definitions
and work.)
8. A) Reparameterize the curve in problem 7. according to
arclength. B) Find the location when one has
traveled a distance of ln2 from 0 on this curve.
9. Given r(t) =
ttt
etete ,cos,sin the Unit Normal Vector. (Show the definitions
and work. This
requires some patience, but does work out.)
10. Find the curvature at t = ln4 on the curve r(t) =
ttt
etete ,cos,sin .
11. Given a cycloid x = a(t – sint) and y = a( 1 – cost) which
the path traced by a point on a rolling circle.
work that proves that the arclength of
one arch is 8a.

4. 12. Stat
2
2),2sin(8),2cos(8)( ttttr .
13. State the domain and ranges of r(t) =
2
2 22
7 2
, ,
8 88
t t
.
14. Find the
2
2 22
7 2
lim , ,
8 88
t
t t
t tt

5. .
15. Find the velocity, acceleration, and speed of a particle with
the given position function.
2
16. Read the parametric equations for trajectory motion on page
889. A projectile is fired with an initial
speed of 180 m/sec and angle of elevation 54º. A) Find the
range of the projectile B) the maximum
height reached and c) the speed at input.
17. Read page 890 and find the tangential and normal
components of the acceleration vector.
2
Running head: Stress In College Students
1
Stress In College Students
2

6. Stress in College Students (Drafted Version)
Name
Professor :
Class
Date:
Stress in College Students
The life of a college student is greatly marked with a high
incidence of stress occurrence. However, not all college
students suffer from stress. The stress response depends on
personal readiness to cope with the demands of the situation and
the situation itself to which one refers. That is, how an
individual responds to stressful events depends on both the
personal disposition of the person and the situation in which
these events happen. Claiming that a college student is suffering
from stress or say one is not suffering is of questionable utility
for its generality. With the development of this paper, one come
to acknowledge more comprehensive academic stress levels
experienced by college students, both having to do with the
particular situations favor its appearance such as in situations
that cause reactions in individuals.
One of the most widely studied factors related to stress in
colleges has been linked to the transition from pre-university
level to the university world. The change or transition from one
environment to another are common features life, however, in
most cases, these changes are associated with stress and even
can have adverse effects on some powerful people, affecting
their personal well-being and overall health. In this regard,
there are well-known scholars ready to demonstrate the
incidence of academic stress on health issues. These changes
are indicators of depression of the immune system and,
therefore, a greater body vulnerability to disease. Other work
confirm changes in the immune response associated with
academic stress, in this case, evidenced by low T cell activity
and response to mitogens.

7. Sometimes, students tend to have a very high level of stress that
can cause serious physical problems and diseases. Furthermore,
most of the underlying causes stress in student’s, are related to
activities of the academic area. For example, a survey
conducted on a hundred students from different races in their
first and second semester, revealed that the five most stressful
events were: failing to understand the teachers, boring classes,
having many things to do, suffering from the desire to deliver
jobs and projects and trying to do well in college. The
accumulation of all these causes with many other similar
student issues created an atmosphere of tense and exhausting
work, where depletion is becoming evident.
Likewise, stress affects not only physically, but also makes one
emotionally and psychologically imbalanced. It is normal for a
person with feelings to react to stress. But then again when
these emotions are more intense, and reactions become
abnormal, they indicate a very high level of stress. The more
exaggerated the response of a person with a stressful situation,
the higher the stress levels will be noted. There are many cases
that are seen daily in the college environment that reflect these
attitudes. For example, when a student suddenly feel anxiety
because they say the next class has an exam, or when they feel
angry because they talk to their friends and do not answer, or
even when mad at them over trifles and things of small
importance, or just when they feel fear because they are accused
of something they did not commit. Similarly, there are other
warning signs of stress, among which one can mention the
feeling of failure, loss of confidence, sadness, guilt, frustration,
indecision, unrest and even thoughts of death and loss of
interest in life. Arguably, these psychological effects can be the
classic symptoms of stress or mental illness. That's true,
although it might be thought that in some cases that mental
illness is an extreme emotional response to stress. Finally, it is
noted that such reactions can lead the student to take fateful

8. decisions that affect them in their academic work.
Stress can influence the economic life of an individual.
According to the research, this continuous exposure to stress
often leads to diseases such as depression, headaches,
dyspepsia, palpitations, loss of appetite and muscle aches. The
origin of these conditions is that when faced with a stressful
situation, the brain, and the body responds by only increasing
the production of certain hormones such as cortisol and
adrenaline. These cause changes in heart rate, blood pressure,
metabolism and physical activity. The worst part is that as time
progresses and if appropriate measures are not taken, these
chronic diseases may turn to the point where they can no longer
be controlled, and one has to resort to a specialist for treatment.
All the effects of stress are reflected in the life of the student. If
one does not have a proper stress management, this can cause
the student's performance to deteriorate. The following is a
hypothetical case where the effects of stress are shown:
Nicholas, a student of Economics and International Business
must take the final exam of a course called Algebra and
Functions. On the other hand, he fails the course and, therefore,
must repeat the test for one more time. He has been studying a
whole week to pass. At the time of examination, he feels very
nervous, has stomach crunches, his pulse accelerates, he has
sweaty hands, his mouth gets dry, feels like going to the
bathroom and his heart beats rapidly. Nicholas presents the test
in these conditions. Later he will claim the test results and
realize that he has failed, and that should do this course again if
he wants to become a professional. Why did he fail the test
considering that he had had an excellent preparation? The
answer is simple: stress. If Nicholas had controlled his anxiety
and felt reassured when sitting for his exam, chances are he
could easily have done it without any mental block,
remembering everything studied and maybe would have passed.
Mishandling of a stressful situation can have far-reaching

9. implications for the training of a person. Admittedly, this might
have happened to many students. It is also for the simple reason
of not knowing how to control their stress.
Assignments, papers, exams, meetings, interviews,
commitments, events, outings with friends, are events that a
college student performs consistently throughout their learning
process. Each of these activities can be a source of stress in the
life of a college student along with many more. However, most
important of all these pressures are the consequences that this
phenomenon brings in students' lives. The stress affects many
areas of a college student’s life either, academic, physical or
psychological hence the need to comprehend its nature.