Elementary analysis
You may work in teams of size no more than three. Each team should hand in
a single homework set, signed by all of the team’s members. All team members will
receive the same score for this homework. The value of this homework set is 15 points.
(**) Unless otherwise directed, you may use results proved in class notes or in Rudin,
but if you do, cite them as [Rudin, Theorem 5.7] or [Class Notes, Theorem 8.3].
(***) Write up your solutions in mathematical English (as in our class notes) and in
publicationready form, preferably typed in some technical word processing language.
1) The comparison test
(which we will prove in class) says if 0
a
n
b
n
for suciently large
n
and if
1
1
b
n
converges, then so does
1
1
a
n
, and furthermore if
1
1
a
n
diverges, then so does
1
1
b
n
.”
Show how to use this test to compare the series
1
2
1
n
2
n
+1
and
1
2
1
n
1
:
5
. This will require you to
prove an inequality.
2) In this problem we will use the comparison test from problem (1) to prove the Limit Comparison Test
which says: Suppose
a
n
>
0 and
b
n
>
0 for all
n
. If lim
n
!1
a
n
b
n
is a positive real number
L
, then
either both
1
1
a
n
and
1
1
b
n
converge, or both series diverge.” Here are the steps:
2a) Given that
a
n
>
0 and
b
n
>
0 and lim
n
!1
a
n
b
n
is a positive real number
L
, explain how we know
that for suciently large
n
, we have 0
<
0
:
5
L <
a
n
b
n
<
1
:
5
L
.
2b) Use 2a) and a comparison test to show that if
1
1
a
n
converges, then so does
1
1
b
n
.
2c) Use 2a) and a comparison test to show that if
1
1
a
n
diverges, then so does
1
1
b
n
2d) Use the limit comparison test to show that
1
2
n
n
3
1
converges. This will require you to specify a
series whose convergence or divergence you already know, and then show that the limit comparison
test applies, and nally make a conclusion about
1
2
n
n
3
1
.
3) The Integral Test
(which we will prove in class) says that if
f
(
x
) is a decreasing nonnegative
continuous function whose domain includes [1
;
1
), then
1
1
f
(
n
)
converges if and only if
lim
T
!1
Z
T
1
f
(
x
)
dx
<
1
:
[Warning: lim
T
!1
R
T
1
f
(
x
)
dx
is sometimes written as
R
1
1
f
(
x
)
dx
but it must be evaluated
using limits rather than trying to use arithmetic with innities.] Use the integral test to determine
convergence or divergence of each of the following. You may assume that the functions involved are
continuous.
3a)
1
1
1
n
1
:
5
3b)
1
2
1
n
log(
n
)
where log(
n
) denotes the natural logarithm of
n
. [Hint: try
u
= log(
x
).]
3c)
1
2
1
n
(log(
n
))
2
56
nursing care plans
To present using one ofthe nursing care plans from assignment 1 and refer to the ANMC
domains in order to identify why and how nurses need to be cultural sensitive when caring for this patient who you can decide could t
nonEnglish speaking background (ARABIC). (10 minutes)
Refer to the ANMC domains in order to identify and discuss why and how nurses need
to practice in relationship to legal and lor ethical issues and to refer to either a health topic or an incident relevant to either a
maternity (eg l/F) or paediatric eventls (eg medication error). (10 minutes)
The tutorial presentation is to be interactive with the
audience but based on sound knowledge and research based evidence and demonstrate correct APA format for in text and endtext
referencing
Evidence of research, using a variety of current credible resources
This will be a total of 20 mins, a power point
type slide show is acceptable however the presentation may be as creative as you like.
A lesson plan and copy of any power points or
any handouts is required to be presented to the tutor on the day of your presentation
Review the marking criteria to achieve maximum marks
for this assessment.
ORDER THIS ESSAY HERE NOW AND GET A DISCOUNT !!!
Our Service Charter

Excellent Quality / 100% PlagiarismFree
We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarismfree. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers. 
Free Revisions
We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed. 
Confidentiality / 100% No Disclosure
We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service. 
Money Back Guarantee
If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 1430 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% moneyback in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit. 
24/7 Customer Support
We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.