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(a) By differentiating the double-angle formula obtain the

Calculus, | 7th Edition | ISBN: 9780538497817 | Authors: James Stewart ISBN: 9780538497817 125

Solution for problem 58 Chapter 2

Calculus, | 7th Edition

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Calculus, | 7th Edition | ISBN: 9780538497817 | Authors: James Stewart

Calculus, | 7th Edition

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Problem 58

(a) By differentiating the double-angle formula obtain the double-angle formula for the sine function. (b) By differentiating the addition formula obtain the addition formula for the cosine function.

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Where do Southeast Asians Live Population distribution is tied to physical geography  On the mainland, most people are concentrated within cities or near the coast  On the islands, most people are concentrated in coastal cities o Examples:  Manila, Philippines, the 15th most populated city in the world  Jakarta, Indonesia, the 17th most populated city in the world Language Families Languages in this region have distributed mainly through spatial interaction (i.e through trade). Spatial Interaction- the flow of process from one location to another Lingua Franca- a language that is adopted as a common vernacular between speakers whose native languages are different  The islands consist of an Austronesian language family o There is a historical connectedness between New Zealand, Hawaii, Madagascar and other islands of South East Asia  Diversity within the indigenous population and lack of spatial interaction within more modern times have caused great linguistic diversity throughout the region o Indonesia alone has more that 600 local languages  Lingua franca: Bahasa  Bahasa was the common language for trade, thus making the adoption of this language reasonable for Indonesians  Also became the language that missionaries of Islam and Christianity came to speak in the region  There is also a WIDE and EXTENSIVE range of ethnic groups in Indonesia Indonesia, Independence, and Language Indonesia recently gained their independence from the Japanese and the Dutch in 1945. Both countries had major effects on language culture in the region, but Indonesian was chosen as the official language. This is because Dutch was only spoken by the MOST educated Indonesians (Indonesians who went away to study in England and came back). Even though "Javanese" was spoken by the largest ethnic group at the time, 87% of the population were already literate in Indonesian. Language in the Philippines  Large amounts of colonial influence: o Spanish language and English versus the local language of Filipino  The Philippines went under their independence movement in the 1800's and had a revolution (The United States aiding them in their revolution) o During this time, the U.S and Spain were having the Spanish American War  Spain lost  We "gained" the Philippines as a "colony"  The Philippines fought for independence from the United States o They eventually won  Government chose Tagalog as the national language o This was the native language of only 21% of the population  This population lived primarily around and in Manila (the capital)  Government removed Tagalog  Filipino was made the national language in the 1980s English throughout the Region o English is a global language used in medicine, academics, trade and politics o Many recognize the importance of the knowing the language  It is key for competing in the global economy o Even students from Russia and Asia are traveling to learn English in the Philippines Religion in the Entire Region Hinduism o Hinduism was one of the first religions to diffuse throughout Southeast Asia during a "universalizing period"  Diffused through the Silk Road trade routes  Brahmin priests who migrated through these routes and resettled in Southeast Asia began teaching these beliefs  These beliefs were originally taught in Sanskrit Buddhism o Theravada branch of Buddhism: influenced by Sri Lanka  Prior to this, evidence suggests that Mahayana was prominent branch of Buddhism in this region o Stupas (temples usually built around a relic of Lord Buddha: hair, bone, foot) were built as sacred sites to the religion -Theravada Buddhism (practiced by 40% of the population) o Originated in northern India  Secondary hearth is located in southern India and Sri Lanka o Diffused to:  Myanmar, Thailand, Laos and Cambodia o Emphasis on the historical teachings of Buddha  The goal was self-liberation and to live a monastic (like the monks) life -Mahayana Buddhism (practice by 56% of the population) o Known as the "Great Vehicle" to broaden its appeal to the natives o Hearth in northern India o Diffused to:  Japan, Korea and Vietnam o Emphasis: individuals achieve enlightenment, which helps all living beings o Follows the teachings of Buddha and bodhisattvas (great spiritual leaders) Islam o Spread through hierarchical diffusion (important trade routes, straits and imports for trade) o "Contagious"- spreads from people living in ports to the people who lived around those port cities and so on o Sultanates increase in hierarchical diffusion o Sultan: governor, political leader of sultanate o Islam is mostly present in the mainland of Malaysia, Brunei and Indonesia Christianity and Animist Religions o Christianity was spread through Arabian Christian traders under the colonial power of the Portuguese  They spread Roman Catholicism to the Philippines and East Timor-Timor-Leste o Animist religions (the belief that animals, plants and inanimate objects posses spiritual essence) belong to the indigenous populations that live in the mountainous and more remote areas  This is more prominent in areas of Malaysia, Brunei, Indonesia and further inland of China o Syncretic religions (the blending of two or more religious beliefs into a new system/religious tradition)

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Textbook: Calculus,
Edition: 7
Author: James Stewart
ISBN: 9780538497817

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(a) By differentiating the double-angle formula obtain the