Calc help *small comp*

Need someone to help with intro calc hw. Small compensation. Shouldn't take more then 15min for someone who knows calc. Pm me your skype.

 

Sequences are to calculus what at calculator is to a scientist. There are many ways to introduce sequences. Here we will follow a somewhat unorthodox way. Indeed, consider a scientist doing an experiment; he is collecting data, let us say, every day. So, put to be the data collected the first day, be the data collected the second day, and so on.... and is the data collected after n days. Clearly, we are generating a set of numbers with a very special characteristic: there is an order on the number, that is, we naturally have the first number, the second number, and so on.... A sequence is by definition a set of real numbers with this natural order. We wil use the notation

,

to describe the sequence of numbers where is the nth number.

Definition (Range): Consider the sequence . The set



is called the range of the sequence.

Of course, in the range there is no order. For example, consider the sequence . Its range is the set . It has two elements. The sequence itself is alternating between 1 and -1.

Consider the sequence . It is clear that we have



The numbers are getting bigger and bigger. Now consider the sequence


.
In this case, we have



Notice that the numbers are getting smaller and smaller. You may wonder, is it always the case that any sequence of numbers will have one of these two behaviors??? The answer is, of course, NO. Indeed, consider the sequence

.

We have

.

One may tend to believe that this sequence is getting bigger and bigger. Wrong!!! Indeed, let us go further. We have

.

See that the tenth number is equal to the ninth. Nothing wrong yet; however, let us compute the eleventh number

.

The tenth number is bigger than the eleventh. The sequence gets bigger and bigger until it reaches the tenth number, then it starts getting smaller and smaller. One may come up with a much simpler example but this example is interesting since most of us would have quit after computing the first five numbers and claim the sequence is getting bigger and bigger!!!!!

Remark: Note that in order to check that the sequence is getting bigger, we need to check that



This will take a lot of time. There is a shorter way to do that. Indeed, if we check that for any , this will be enough. An inductive argument will convince you, I hope....

Definitions: Consider the sequence . We will say that is

increasing, if and only if, for any , or
decreasing, if and only if, for any .
If one of these properties holds, we say that the sequence is monotonic.
Example: Check that the sequence is increasing.

Answer: Let . We have . Since 2 > 1, then , which gives

.

Example: Check that the sequence is decreasing.

Answer: Let . We have n < n+1. Therefore,



holds.

Remark: It may happen sometimes that the sequence is increasing, if and only if, for any , and decreasing, if and only if, for any . The reader should not panic. No harm will be done.

Now, let us go back to our scientist who collected data every day and where represents the data collected after n days. What if our scientist discovers that the data of the first seven days are not good? Then he has to throw them out. In this case, he has a new sequence of numbers: . We will use the notation

.

In fact, another way to rewrite this new sequence is

.

Clearly, the sequence



represents the case when our scientist throws out the data collected the first k days. This sequence will be referred to as the tail of the original sequence. Also the first k element of the sequence is known as the first block of size k. Using this we see then that the sequence



is decreasing after we throw out the first block of size 9, that is, the tail



is decreasing. Note that we did not check this one before. So it maybe a good idea to train yourself on these kinds of questions.

Remark: Note that there are examples of sequences which do not have a monotonic tail. For example, the sequence is one of them. It alternates forever between the two numbers 1 and -1.

There is another way of checking whether a sequence has a monotonic tail. This happens whenever the sequence is defined by a function. For example, consider the sequence

.

It is not clear or, at least, obvious that this sequence will have a monotonic tail. The reason is that while n grows, the numerator also grows!! Consider the function

,

and compute the derivative

.

It is clear that f'(x) < 0, whenever x > e. Since n > e, for any , then the tail

,

is decreasing.
Definitions: Consider the sequence . We will say that is

bounded above, if and only if, there exists a number M such that
,

for any . The number M is called an upper-bound.
Furthermore, we will say that is bounded below, if and only if, there exists a number m such that
,

for any . The number m is called a lower-bound.

If both of these properties hold we say that the sequence is bounded (in short bd).
Example: The sequence is bounded below by 0 (because it is positive). It is not bounded above.
Example: The sequence is bounded. Indeed, we have for any ,

.

Therefore, 0 is a lower-bound and 1 is an upper-bound.
Useful Remark: The first block of a sequence is always bounded regardless of its size because we are dealing with finitely many numbers. Therefore, a sequence is bounded (below, above or both), if and only if, one of its tail is bounded (below, above or both).

 

Tom Coates (born 19 July 1972) is a technologist and early weblogger based in San Francisco, California who has been writing plasticbag.org since 1999. He has written extensively about social software, the web of data, location services and future media distribution and launched the Fire Eagle location service for Yahoo in 2008.
Coates was educated at the Norwich School, the University of Bristol and the London College of Printing. He worked at the BBC running an R&D team for BBC Radio, and before that he developed the geo-coded online community UpMyStreet Conversations.[1] He has also developed online communities for emap and was Production Editor of Time Out's website.[2] His professional written work includes film reviews for the BBC,[3] contributions to Time Out city guides and comment pieces on technology for The Guardian.[4]
From late 2005 until 14 May 2010 Coates worked for Yahoo!, initially for the Tech Development team with Caterina Fake, Jeremy Zawodny and Simon Willison.[5] and later as Head of Product for the Brickhouse product incubator.[6]
Coates' weblog has won a number of Bloggies including Best European Weblog (2001 and 2002),[7][8] Best Gay/Lesbian/Trans weblog (2001),[7] Best British or Irish Weblog (2004 and 2005)[9][10] Lifetime Achievement (2005).[10] He also runs the online subcultural community Barbelith - initially inspired by the work of comic book writer Grant Morrison.[11]
He is also on the advisory council of the Open Rights Group.
Coates co-organised the London Hack Day in June 2007 with help from Matthew Cashmore from backstage.bbc.co.uk.[12]
The Evening Standard named Coates as one of the Most Influential 1000 Londoners in October 2007 and again in October 2008.[13][14]
In March 2008, Coates launched the Fire Eagle location brokerage service for Yahoo! at ETech. The service was opened up to the general public on August 12, 2008. Despite being well regarded as a significant contribution to location sharing and online privacy, the service was generally unsuccessful. Tom Coates has since left Yahoo.
In January 2011 he was listed in Wired UK's Smart List 2011.[15]
He is an advisor for several start-ups including Lanyrd, the social conference directory created by Simon Willison and Natalie Downe.[16] and founder of Product Club, a company that bills itself as doing "New Product Development and Invention".

 

Pope&#8217;s life as a writer falls into three periods, answering fairly enough to the three reigns in which he worked. Under Queen Anne he was an original poet, but made little money by his verses; under George I. he was chiefly a translator, and made much money by satisfying the French-classical taste with versions of the &#8220;Iliad&#8221; and &#8220;Odyssey.&#8221; Under George I. he also edited Shakespeare, but with little profit to himself; for Shakespeare was but a Philistine in the eyes of the French-classical critics. But as the eighteenth century grew slowly to its work, signs of a deepening interest in the real issues of life distracted men&#8217;s attention from the culture of the snuff-box and the fan. As Pope&#8217;s genius ripened, the best part of the world in which he worked was pressing forward, as a mariner who will no longer hug the coast but crowds all sail to cross the storms of a wide unknown sea. Pope&#8217;s poetry thus deepened with the course of time, and the third period of his life, which fell within the reign of George II., was that in which he produced the &#8220;Essay on Man,&#8221; the &#8220;Moral Essays,&#8221; and the &#8220;Satires.&#8221; These deal wholly with aspects of human life and the great questions they raise, according throughout with the doctrine of the poet, and of the reasoning world about him in his latter day, that &#8220;the proper study of mankind is Man.&#8221;

Wrongs in high places, and the private infamy of many who enforced the doctrines of the Church, had produced in earnest men a vigorous antagonism. Tyranny and unreason of low-minded advocates had brought religion itself into question; and profligacy of courtiers, each worshipping the golden calf seen in his mirror, had spread another form of scepticism. The intellectual scepticism, based upon an honest search for truth, could end only in making truth the surer by its questionings. The other form of scepticism, which might be traced in England from the low-minded frivolities of the court of Charles the Second, was widely spread among the weak, whose minds flinched from all earnest thought. They swelled the number of the army of bold questioners upon the ways of God to Man, but they were an idle rout of camp-followers, not combatants; they simply ate, and drank, and died.

In 1697, Pierre Bayle published at Rotterdam, his &#8220;Historical and Critical Dictionary,&#8221; in which the lives of men were associated with a comment that suggested, from the ills of life, the absence of divine care in the shaping of the world. Doubt was born of the corruption of society; Nature and Man were said to be against faith in the rule of a God, wise, just, and merciful. In 1710, after Bayle&#8217;s death, Leibnitz, a German philosopher then resident in Paris, wrote in French a book, with a title formed from Greek words meaning Justice of God, Theodicee, in which he met Bayle&#8217;s argument by reasoning that what we cannot understand confuses us, because we see only the parts of a great whole. Bayle, he said, is now in Heaven, and from his place by the throne of God, he sees the harmony of the great Universe, and doubts no more. We see only a little part in which are many details that have purposes beyond our ken. The argument of Leibnitz&#8217;s Theodicee was widely used; and although Pope said that he had never read the Theodicee, his &#8220;Essay on Man&#8221; has a like argument. When any book has a wide influence upon opinion, its general ideas pass into the minds of many people who have never read it. Many now talk about evolution and natural selection, who have never read a line of Darwin.

In the reign of George the Second, questionings did spread that went to the roots of all religious faith, and many earnest minds were busying themselves with problems of the state of Man, and of the evidence of God in the life of man, and in the course of Nature. Out of this came, nearly at the same time, two works wholly different in method and in tone&#8212;so different, that at first sight it may seem absurd to speak of them together. They were Pope&#8217;s &#8220;Essay on Man,&#8221; and Butler&#8217;s &#8220;Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature.&#8221;

Butler&#8217;s &#8220;Analogy&#8221; was published in 1736; of the &#8220;Essay on Man,&#8221; the first two Epistles appeared in 1732, the Third Epistle in 1733, the Fourth in 1734, and the closing Universal Hymn in 1738. It may seem even more absurd to name Pope&#8217;s &#8220;Essay on Man&#8221; in the same breath with Milton&#8217;s &#8220;Paradise Lost;&#8221; but to the best of his knowledge and power, in his smaller way, according to his nature and the questions of his time, Pope was, like Milton, endeavouring &#8220;to justify the ways of God to Man.&#8221; He even borrowed Milton&#8217;s line for his own poem, only weakening the verb, and said that he sought to &#8220;vindicate the ways of God to Man.&#8221; In Milton&#8217;s day the questioning all centred in the doctrine of the &#8220;Fall of Man,&#8221; and questions of God&#8217;s Justice were associated with debate on fate, fore-knowledge, and free will. In Pope&#8217;s day the question was not theological, but went to the root of all faith in existence of a God, by declaring that the state of Man and of the world about him met such faith with an absolute denial. Pope&#8217;s argument, good or bad, had nothing to do with questions of theology. Like Butler&#8217;s, it sought for grounds of faith in the conditions on which doubt was rested. Milton sought to set forth the story of the Fall in such way as to show that God was love. Pope dealt with the question of God in Nature, and the world of Man.

 

1 plus 1 equals = 2

ill pm you my pp email

 

welcome nigga, don't even have to send me cash im just doing it for the karma

 

look outside your cars on fire, that's karma for you.

 

i got fire insurance son ill get paid out $15,000

 

somebody wants mod lelele -.-

 

dont need to try to step at me like that fendle i gotchu man. non disrespect

 

i gotchu too bro

 

listen i know u been having a hard time lately call me any time

 

Post the question in here, I can't access skype at the moment, but I should hopefully be able to give you some insights. Are you working with derivatives?

 

Here: (http://s9.postimage.org/tyusr2ttr/help.png)

I am not sure how to find the prime limits (i believe thats what is being asked) of the ones with a - on the right.

 

mod me pl0x

 

4
4
4
3
Nonexistent
-1


-.-.-.-.-..-.-.-..-.-.

 

virgy's cant even calculus these days -.---

 

fish fash flash

 

Fishys wrong don't listen

 

virgy who calls others virgy can't even post the correct answer.