LIMITS AND CONTINUITY 1. The concept of limit x2 − 4 . Examine the behavior of f (x) as x approaches 2. Example 1.1. Let f (x) = x−2 Solution. Let us compute some values of f (x) for x close to 2‚ as in the tables below. We see from the first table that f (x) is getting closer and closer to 4 as x approaches 2 from the left side. We express this by saying that “the limit of f (x) as x approaches 2 from left is 4”‚ and write x→2− lim f (x) = 4. Similarly‚ by looking at the second table
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Change‚ something we want but doesn’t always come easy to us. Positive change is what can improve conditions‚ lives and in turn increase the happiness of a person. America in 1900 was a place needing improvement. Something needed to be done but people had a difference in opinion of how effectively execute actions that would bring change. The expansion of government power and power of the president caused the necessary change needed in the progressive era. Cooperations were a block to people’s pursuit
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Before the era of 1200-1450‚ developed countries and religions were changing and cultures molded how empires operated. The Silk Road opened‚ countries were in their infancy‚ and religions like Christianity were developing with the lifetime of Jesus Christ. As time went by‚ traveling for reasons other than religion started‚ and people started developing empires and long-distance trade. During the 12-1400s‚ new empires started trading with people close to them geographically‚ trading across continents
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used which left lot of economic opportunity to be had. During the time between 1450 and 1750‚ the new world was just starting to be settled by Europeans‚ starting with Columbus reaching the Americas in 1492 (when he sailed the ocean blue). This period was used by the Europeans to conquer any empires and enslave workers to work there new empires and mines in the search for precious metals. Later in the time from 1750-1900 the economies of the new economies became strongly focused on agriculture.
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During the period between 1450-1750‚ Western Europe has gone through various religious upheavals and drastic changes. Some of these changes have led to conflict‚ often bloody‚ and subsequently shifts of power within the West. In contrast‚ some of these changes have also led to the technological advancement of the West and the eventual world dominance of Western Europeans in economics‚ politics‚ and innovation. These revolutionary changes and eras include the Renaissance‚ Protestant Reformation‚ the
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efforts‚ to restore the unity‚ the security‚ the stability of the empire. They are famous figures in politics‚ religion‚ and art. The Roman Empire from 100 C.E. – 600 C.E. had many cultural and political changes as well as cultural and political continuities. There were many political changes from the Roman Empire to the Byzantine Empire. The Roman Empire had a Republic government where the power resided in an assembly of male citizens where the senate made policy and governed. The senate brought
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Over time‚ a culture’s art will change or improve in some way. Some characteristics may remain the same while other characteristics change drastically. Art in the Archaic era and the Classical era had no emotion and unrealistic features‚ but the Classical era brought a sense of anatomy and movement to its art. In the Archaic era and Classical era‚ emotion was not present in art. Characters had plain expressions on their faces; their eyes told nothing‚ regardless of what they were doing. The
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1450-1750 Review What were the major changes/developments from 1450 – 1750? 1450-1750 Major Developments European discovery of Americas creates a New Global Economy which begins a process of globalization Atlantic Trade Network (Triangular Trade) Atlantic Slave Trade Major Biological Exchanges (Columbian Exchange) New Empires in Asia‚ Africa‚ Europe and Americas Gunpowder Empires Colonial administrations Coercive labor systems Slave Systems Rise of Europe Scientific Revolution Enlightenment
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Political Changes and Continuities in China Through 600 CE Up until the 7th century CE‚ Chinese politics mainly remained the same after the Han dynasty. The major differences had to do with the way that the people were governed and how much influence religion had over the government. Before the Han‚ there was the Zhou and Qin dynasties‚ the Zhou was the first to implement the basis of any widespread government‚ and it is also the first example of continuity during the classical period in China
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600-1450 C.E. 27. Where and when did the Kush and Axum civilizations develop‚ and what were their major industries for trade? The Kush and Axum civilizations developed to the south of Egypt in the upper reaches of the Nile river. Kush developed at about the same time as ancient Egypt‚ and at one point around 750 B.C.E. actually conquered it. Less than a hundred years later‚ however‚ Kush retreated southward back to its capital at Meroe‚ where it became the center of ironworks and trade. After the
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