What does a limit in calculus measure?

The tendency of a function as the input approaches a certain value.

The minimum value of a function.

The maximum value of a function.

The average value of a function.

What does it mean when the limit of a function does not exist?

The function does not approach a single value as the input approaches a specific value.

The function approaches zero as the input approaches a certain value.

The function approaches infinity as the input approaches a certain value.

The function approaches a constant value as the input approaches a certain value.

What is the definition of a one-sided limit?

The limit of a function as the input approaches a certain value from one side (either the left or the right).

The highest value that a function can reach.

The lowest value that a function can reach.

The average value of a function over a certain interval.

Limits in calculus

Democratic Constitution in South Africa Struggle against Apartheid • Apartheid was the name of a system of racial discrimination unique to South Africa. • This system was particularly oppressive for the blacks. → They were forbidden from living in white areas. • Since 1950, the blacks, coloured and Indians fought against the apartheid system. • The African National Congress (ANC) was the umbrella organisation that led the struggle against the policies of segregation. • In 1964, Nelson Mandela and seven other leaders were sentenced to life imprisonment in 1964 for daring to oppose the apartheid regime in his country. Towards a New Constitution • As protests and struggles against apartheid had increased, the white regime changed its policies. • After 28 years of imprisonment, Nelson Mandela released from jail. • At the midnight of 26 April 1994, democracy was adopted as a form of government in South Africa. • After two years, a constitution came out which gave to its citizens the most extensive rights available in any country. Why do we need a Constitution? • A constitution is necessary because: → It generates a degree of trust and coordination that is necessary for different kind of people to live together. → It specifies how the government will be constituted, who will have power to take which decisions. → It lays down limits on the powers of the government and tells us what the rights of the citizens are. → It expresses the aspirations of the people about creating a good society. Making of the Indian Constitution • In 1928, Motilal Nehru and eight other Congress leaders drafted a constitution for India. • In 1931, the resolution at the Karachi session of the Indian National Congress dwelt on how independent India’s constitution should look like. • Factors contributed to the making of our Constitution. → Ideals of French Revolution → The practice of parliamentary democracy in Britain → The Bill of Rights in the US → The socialist revolution in Russia The Constituent Assembly • In July 1946, Elections to the Constituent Assembly were held. → The drafting of the document called the constitution was done Constituent Assembly. → Dr. Rajendra Prasad was the Chairman of the Constituent Assembly. → In December 1946, the first meeting was held. • After the country was divided into India and Pakistan, the Constituent Assembly also got divided. • The Assembly adopted the Constitution on 26 November 1949 but it came into effect on 26 January 1950. • To mark this day we celebrate January 26 as Republic Day every year. • The Constituent Assembly worked in a systematic, open and consensual manner. → First some basic principles were decided and agreed upon. → Then a Drafting Committee chaired by Dr. B.R. Ambedkar prepared a draft constitution for discussion. → More than two thousand amendments were considered. Philosophy of the Constitution • The Constitution begins with a short statement of its basic values which is called the Preamble to the constitution. The preamble focuses on: → Justice, social, economic and political. → Liberty of thoughts, expression, belief, faith and worship. → Equality of status and of opportunity. → Fraternity assuring the dignity of the individual and the unity and integrity of the nation.

Spectacular - Spektakulär Unexpected - Oväntad A moment of truce - Ett vapenstillestånd Push the limits - Tänja på gränserna Free climber - Fria klättrare Descriptions - Beskrivningar Get a rush from - Få en kick från End up face to face with sharks - Sluta ansikte mot ansikte med hajar Crawling - Krypande Chalk powder - Kritpulver Pouch around your waist - Påse runt din midja On purpose - Med avsikt Seek thrills - Söka spänningar Accomplish my dreams - Uppnå mina drömmar Comes at a cost - Kommer med ett pris Permission - Tillstånd Achievements - Framgångar Fallen from heights - Fallit från höjder Fallen into a coma - Hamnat i koma Stiches - Stygn Target - Mål Reaching his goal - Nå sitt mål Retell - Berätta om Ordinary people - Vanliga människor Uncommon - Ovanlig On American soil - På amerikansk mark Hijacked - Kapat The outcome - Resultatet The public - Allmänheten Structural engineer - Byggnadsingenjör Port - Hamn Witnessing - Vittna Make it down the stairwell - Ta sig ner för trapphuset A roaring sound - Ett brölande ljud Take cover - Söka skydd Crouched down - Hopkrupen The walls cracked open - Väggarna sprack upp Underneath - Under Fall unconscious - Förlora medvetandet In the rubble - I rasmassorna Unaware of - Omedveten om Devastating moment in history - Förödande ögonblick i historien The mobile network is down - Mobilnätverket ligger nere Commit crimes - Begå brott Throughout history - Genom historien Path - Väg Whiny voice - Gnällig röst Wearing him down - Slita ner honom Long for - Längta efter Thumping - Dunkande Spiked with a deadly dose of poison - Spetsad med en dödlig dos gift Gone through with it - Genomfört det Constant nagging - Ständigt gnäll Infidelity - Otrohet Carved - Skuren Perform on the big stages - Uppträda på de stora scenerna Unrealistic demands - Orealistiska krav Something fishy is going on - Något skumt pågår Offered a reward - Erbjöd en belöning Downfall - Fall Accomplice - Medbrottsling Undoubtedly - Utan tvekan Board a ship - Stiga ombord på ett skepp Suspense - Spänning Trip on a wire - Snubbla på en tråd Invention - Uppfinning Customs officer - Tulltjänsteman Extraordinary - Extraordinär Nearly - Nästan The entire population - Hela befolkningen Cease to exist - Upphöra att existera Great courage - Stort mod Goodwill - God vilja A little bit of humanity - Lite mänsklighet In the midst - Mitt ibland Lose faith in - Förlora tro på Snowflakes - Snöflingor Turn the doorknob - Vrida dörrknoppen Shelter - Skydd Gesture towards the cabin - Gesta mot stugan Pale - Blek Commotion - Uppståndelse Medic - Sjukvårdare Ease up the tension - Minska spänningen Extend his hand - Sträcka ut sin hand Painkillers - Smärtstillande Supper - Kvällsmat Foolish - Dum Establish - Etablera Drop a nuclear bomb - Släppa en kärnvapenbomb The Great Plague - Den stora pesten Civil rights - Medborgerliga rättigheter Underline - Understryka Keen on - Angelägen om

. Video games are a popular pastime for teenagers (and many adults) all around the world. In fact, 97% of American teenagers play video games. Not all video games show graphic violence. But about half of the top selling video games do. It is common for a video game to include weapons that are used to harm other humans. Many video game critics argue that violent images and violent role play in video games can desensitize teens to violence. This means that violence starts to seem normal. Some argue that enough violent video games can even make teenagers more likely to commit violent acts in real life. In 1993, Congress first took a look at the issue. Mortal Kombat had just been released. Many Americans were worried about children playing such a violent game. Congress talked a bout whether the government should place limits on the sale of video games. This caused the video game industry to create an organization to rate video games. This organization is called the Entertainment Software Rating Board. They give ratings based on the age level a video game is appropriate for. The American Psychological Association (APA) created a Task Force on Violent Media. In 2017 they released a statement. It labeled violent video games as a “risk factor for aggression.” This means that they linked playing video games to increased “aggressive behaviors, thoughts and emotions” and “decreased empathy.” Empathy is the ability to understand the feelings of others. But they did not actually state that video games are the cause of an increase in crime. Plus, other studies have said that the competition in video games increases aggression more than just violent images.

Cells of different organisms and even cells within the same organism are very diverse in terms of shape, size, and internal organization. One theme that occurs again and again throughout biology is that form follows function. In other words, a cell’s function influences its physical features. Cell Shape The diversity in cell shapes reflects the different functions of cells. Compare the cell shapes shown in Figure 4-4. The long extensions that reach out in various directions from the nerve cell shown in Figure 4-4a allow the cell to send and receive nerve impulses. The flat, platelike shape of skin cells in Figure 4-4b suits their function of covering and protecting the surface of the body. As shown below, a cell’s shape can be simple or complex depending on the function of the cell. Each cell has a shape that has evolved to allow the cell to perform its function effectively. SECTION 2 OBJECTIVES ● Explain the relationship between cell shape and cell function. ● Identify the factor that limits cell size. ● Describe the three basic parts of a cell. ● Compare prokaryotic cells and eukaryotic cells. ● Analyze the relationship among cells, tissues, organs, organ systems, and organisms. VOCABULARY plasma membrane cytoplasm cytosol nucleus prokaryote eukaryote organelle tissue organ organ system Cells have various shapes. (a) Nerve cells have long extensions. (b) Skin cells are flat and platelike. (c) Egg cells are spherical. (d) Some bacteria are rod shaped. (e) Some plant cells are rectangular. FIGURE 4-4 (a) Nerve cell (b) Skin cells (c) Egg cell (d) Bacterial cells (e) Plant cells Copyright © by Holt, Rinehart and Winston. All rights reserved. 1. All cubes have volume and surface area. The total surface area is equal to the sum of the areas of each of the six sides (area = length X width). 2. If you split the first cube into eight smaller cubes, you get 48 sides. The volume remains constant, but the total surface area doubles. 3. If you split each of the eight cubes into eight smaller cubes, you have 64 cubes that together contain the same volume as the first cube. The total surface area, however, has doubled again. CELL STRUCTURE AND FUNCTION 73 Cell Size Cells differ not only in their shape but also in their size. A few types of cells are large enough to be seen by the unaided human eye. For example, the nerve cells that extend from a giraffe’s spinal cord to its foot can be 2 m (about 6 1/2 ft) long. A human egg cell is about the size of the period at the end of this sentence. Most cells, how- ever, are only 10 to 50 μm in diameter, or about 1/500 the size of the period at the end of this sentence. The size of a cell is limited by the relationship of the cell’s outer surface area to its volume, or its surface area–to-volume ratio. As a cell grows, its volume increases much faster than its surface area does, as shown in Figure 4-5. This trend is important because the materials needed by a cell (such as nutrients and oxygen) and the wastes produced by a cell (such as carbon dioxide) must pass into and out of the cell through its surface. If a cell were to become very large, the volume would increase much more than the surface area. Therefore, the surface area would not allow materials to enter or leave the cell quickly enough to meet the cell’s needs. As a result, most cells are microscopic in size. Comparing Surface Cells Materials microscope, prepared slides of plant (dicot) stem and ani- mal (human) skin, pencil, paper Procedure Examine slides by using medium magnification (100). Observe and draw the sur- face cells of the plant stem and the animal skin. Analysis How do the surface cells of each organism differ from the cells beneath the surface cells? What is the function of the surface cells? Explain how surface cells are suited to their function based on their shape. Quick Lab Small cells can exchange substances more readily than large cells because small objects have a higher surface area–to-volume ratio. FIGURE 4-5 mb06se_csfs02.qxd 5/18/07 10:54 AM Page 73 74 CHAPTER 4 BASIC PARTS OF A CELL Despite the diversity among cells, three basic features are common to all cell types. All cells have an outer boundary, an interior sub- stance, and a control region. Plasma Membrane The cell’s outer boundary, called the plasma membrane (or the cell membrane), covers a cell’s surface and acts as a barrier between the inside and the outside of a cell. All materials enter or exit through the plasma membrane. The surface of a plasma mem- brane is shown in Figure 4-6a. Cytoplasm The region of the cell that is within the plasma membrane and that includes the fluid, the cytoskeleton, and all of the organelles except the nucleus is called the cytoplasm. The part of the cytoplasm that includes molecules and small particles, such as ribosomes, but not membrane-bound organelles is the cytosol. About 20 percent of the cytosol is made up of protein. Control Center Cells carry coded information in the form of DNA for regulating their functions and reproducing themselves. The DNA in some types of cells floats freely inside the cell. Other cells have a mem- brane-bound organelle that contains a cell’s DNA. This membrane- bound structure is called the nucleus. Most of the functions of a eukaryotic cell are controlled by the cell’s nucleus. The nucleus is often the most prominent structure within a eukaryotic cell. It maintains its shape with the help of a protein skeleton called the nuclear matrix. The nucleus of a typical animal cell is shown in

41) cavort – v. dance around excitedly 42) censorious – adj. critical of others 43) circumlocution – n. using many words, particularly in an evasive way 44) circumscribe – v. restrict within limits 45) clamor – n. a loud and confused noise 46) clout – n. influence or power 47) cognizant – adj. having knowledge of 48) commensurate – adj. equal to 49) comparable – adj. similar to another thing 50) complement – v. add to or make complete

Angels are spiritual beings. They do not have physical bodies. They are His servants; they obey God and do His will. Angels appear to people only when God has a purpose for them to be seen. People have entertained angels without being aware of it because the angels took on the appearance of ordinary men. They have appeared to people as bright and shining beings. In the Bible, angels have told people not to be afraid. Fallen angels, or demons, rebelled against God and followed Satan. As a result, they were cast out of heaven. The devil, or Satan, is one of these fallen angels. He is God's enemy. Satan was created as a beautiful angel, but his pride led to his downfall. God is infinitely more powerful than Satan, and God has set limits on Satan's temporary power on the earth. Satan tempts Christians to sin and causes some trouble in their life. However, Christians have various ways of overcoming temptation and staying true to the Lord despite the trouble. Being tempted to sin is not a sin; even Jesus was tempted but He never sinned. Christians are tempted by the devil, by their sinful nature, and by other people. Some of the ways that Christians can overcome temptation are by fleeing tempting situations, memorizing and applying Bible verses, exercising self-control, and keeping strong in their faith and their relationship with God.

Fed. 51: To the People of the State of New York: TO WHAT expedient, then, shall we finally resort, for maintaining in practice the necessary partition of power among the several departments, as laid down in the Constitution? The only answer that can be given is, that as all these exterior provisions are found to be inadequate, the defect must be supplied, by so contriving the interior structure of the government as that its several constituent parts may, by their mutual relations, be the means of keeping each other in their proper places. Without presuming to undertake a full development of this important idea, I will hazard a few general observations, which may perhaps place it in a clearer light, and enable us to form a more correct judgment of the principles and structure of the government planned by the convention. In order to lay a due foundation for that separate and distinct exercise of the different powers of government, which to a certain extent is admitted on all hands to be essential to the preservation of liberty, it is evident that each department should have a will of its own; and consequently should be so constituted that the members of each should have as little agency as possible in the appointment of the members of the others. Were this principle rigorously adhered to, it would require that all the appointments for the supreme executive, legislative, and judiciary magistracies should be drawn from the same fountain of authority, the people, through channels having no communication whatever with one another. Perhaps such a plan of constructing the several departments would be less difficult in practice than it may in contemplation appear. Some difficulties, however, and some additional expense would attend the execution of it. Some deviations, therefore, from the principle must be admitted. In the constitution of the judiciary department in particular, it might be inexpedient to insist rigorously on the principle: first, because peculiar qualifications being essential in the members, the primary consideration ought to be to select that mode of choice which best secures these qualifications; secondly, because the permanent tenure by which the appointments are held in that department, must soon destroy all sense of dependence on the authority conferring them. It is equally evident, that the members of each department should be as little dependent as possible on those of the others, for the emoluments annexed to their offices. Were the executive magistrate, or the judges, not independent of the legislature in this particular, their independence in every other would be merely nominal. But the great security against a gradual concentration of the several powers in the same department, consists in giving to those who administer each department the necessary constitutional means and personal motives to resist encroachments of the others. The provision for defense must in this, as in all other cases, be made commensurate to the danger of attack. Ambition must be made to counteract ambition. The interest of the man must be connected with the constitutional rights of the place. It may be a reflection on human nature, that such devices should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions. This policy of supplying, by opposite and rival interests, the defect of better motives, might be traced through the whole system of human affairs, private as well as public. We see it particularly displayed in all the subordinate distributions of power, where the constant aim is to divide and arrange the several offices in such a manner as that each may be a check on the other that the private interest of every individual may be a sentinel over the public rights. These inventions of prudence cannot be less requisite in the distribution of the supreme powers of the State. But it is not possible to give to each department an equal power of self-defense. In republican government, the legislative authority necessarily predominates. The remedy for this inconveniency is to divide the legislature into different branches; and to render them, by different modes of election and different principles of action, as little connected with each other as the nature of their common functions and their common dependence on the society will admit. It may even be necessary to guard against dangerous encroachments by still further precautions. As the weight of the legislative authority requires that it should be thus divided, the weakness of the executive may require, on the other hand, that it should be fortified. An absolute negative on the legislature appears, at first view, to be the natural defense with which the executive magistrate should be armed. But perhaps it would be neither altogether safe nor alone sufficient. On ordinary occasions it might not be exerted with the requisite firmness, and on extraordinary occasions it might be perfidiously abused. May not this defect of an absolute negative be supplied by some qualified connection between this weaker department and the weaker branch of the stronger department, by which the latter may be led to support the constitutional rights of the former, without being too much detached from the rights of its own department? If the principles on which these observations are founded be just, as I persuade myself they are, and they be applied as a criterion to the several State constitutions, and to the federal Constitution it will be found that if the latter does not perfectly correspond with them, the former are infinitely less able to bear such a test. There are, moreover, two considerations particularly applicable to the federal system of America, which place that system in a very interesting point of view. First. In a single republic, all the power surrendered by the people is submitted to the administration of a single government; and the usurpations are guarded against by a division of the government into distinct and separate departments. In the compound republic of America, the power surrendered by the people is first divided between two distinct governments, and then the portion allotted to each subdivided among distinct and separate departments. Hence a double security arises to the rights of the people. The different governments will control each other, at the same time that each will be controlled by itself. Second. It is of great importance in a republic not only to guard the society against the oppression of its rulers, but to guard one part of the society against the injustice of the other part. Different interests necessarily exist in different classes of citizens. If a majority be united by a common interest, the rights of the minority will be insecure. There are but two methods of providing against this evil: the one by creating a will in the community independent of the majority that is, of the society itself; the other, by comprehending in the society so many separate descriptions of citizens as will render an unjust combination of a majority of the whole very improbable, if not impracticable. The first method prevails in all governments possessing an hereditary or self-appointed authority. This, at best, is but a precarious security; because a power independent of the society may as well espouse the unjust views of the major, as the rightful interests of the minor party, and may possibly be turned against both parties. The second method will be exemplified in the federal republic of the United States. Whilst all authority in it will be derived from and dependent on the society, the society itself will be broken into so many parts, interests, and classes of citizens, that the rights of individuals, or of the minority, will be in little danger from interested combinations of the majority. In a free government the security for civil rights must be the same as that for religious rights. It consists in the one case in the multiplicity of interests, and in the other in the multiplicity of sects. The degree of security in both cases will depend on the number of interests and sects; and this may be presumed to depend on the extent of country and number of people comprehended under the same government. This view of the subject must particularly recommend a proper federal system to all the sincere and considerate friends of republican government, since it shows that in exact proportion as the territory of the Union may be formed into more circumscribed Confederacies, or States oppressive combinations of a majority will be facilitated: the best security, under the republican forms, for the rights of every class of citizens, will be diminished: and consequently the stability and independence of some member of the government, the only other security, must be proportionately increased. Justice is the end of government. It is the end of civil society. It ever has been and ever will be pursued until it be obtained, or until liberty be lost in the pursuit. In a society under the forms of which the stronger faction can readily unite and oppress the weaker, anarchy may as truly be said to reign as in a state of nature, where the weaker individual is not secured against the violence of the stronger; and as, in the latter state, even the stronger individuals are prompted, by the uncertainty of their condition, to submit to a government which may protect the weak as well as themselves; so, in the former state, will the more powerful factions or parties be gradnally induced, by a like motive, to wish for a government which will protect all parties, the weaker as well as the more powerful. It can be little doubted that if the State of Rhode Island was separated from the Confederacy and left to itself, the insecurity of rights under the popular form of government within such narrow limits would be displayed by such reiterated oppressions of factious majorities that some power altogether independent of the people would soon be called for by the voice of the very factions whose misrule had proved the necessity of it. In the extended republic of the United States, and among the great variety of interests, parties, and sects which it embraces, a coalition of a majority of the whole society could seldom take place on any other principles than those of justice and the general good; whilst there being thus less danger to a minor from the will of a major party, there must be less pretext, also, to provide for the security of the former, by introducing into the government a will not dependent on the latter, or, in other words, a will independent of the society itself. It is no less certain than it is important, notwithstanding the contrary opinions which have been entertained, that the larger the society, provided it lie within a practical sphere, the more duly capable it will be of self-government. And happily for the REPUBLICAN CAUSE, the practicable sphere may be carried to a very great extent, by a judicious modification and mixture of the FEDERAL PRINCIPLE. PUBLIUS.

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