The Canadian Town of Cheltenham :: Canada

The Canadian Town of Cheltenham Section A - Cheltenham is situated in the town of Caledon. Cheltenham was found in 1822 by Charles Haines. Cheltenham is found near the Credit River furthermore, the Canadian National Railway known as the C.N.R. The total area of Cheltenham is 43 45' North and 79 55' West. The setting of Cheltenham is a valley with the Nigara Escarpment behind it. Cheltenham is situated at the south west purpose of Caledon. Cheltenham is found north of Toronto. Presently in 1989 Cheltenham is for the most part private. There is some open space yet next to no industry now. There is one general store situated in the focal point of cheltenham. There is a cemetary situated inverse of The Fire Lobby. Cheltenham was picked as a town in view of the Credit River and the Canadian National Railway. The railroad delivered trasportation for merchandise to be conveyed to different urban communities. The modest proficient rail transportation too ment that Cheltenham's organizations needed to go up against products made by large scale manufacturing in bigger urban focuses toward the south. In this manner the economy of Cheltenham would rise. The Credit River produce loads of Hydro electric force for the individuals of Cheltenham. The two principle reasons why the site was picked for a town was the transportation delivered by the C.N.R. what's more, the hydro electric created from the Credit River. Part B - The land use at the factory lake territory between 1850-1870 in Cheltenham was for the most part modern employments. The vast majority of the ventures or structures were found exceptionally near one another on the grounds that they all relied upon one another. The enterprises in Cheltenham were found near the Credit stream.

Is the U.S. Winning the Drug War in Latin America Research Paper

Is the U.S. Winning the Drug War in Latin America - Research Paper Example CON: No the U.S. isn't winning the war on drugs in Latin America because†¦ 1. War on drugs has been a misuse of valuable time and assets that could have been put to more readily utilize somewhere else 2. The war on drugs has been risky for the Latin American governments explicitly as they are ones being exposed to mass homicides and brutality more than ever 3. War has prompted debilitated foundations and social flimsiness in these nations prompting more squirm space for these cartels 4. As indicated by the figures, utilization of illicit medications has consistently expanded in the United States. The United States Secretary of Homeland Security Janet Napolitano accepts that the war on drugs is a triumph. As indicated by her I would not concur with the reason that the medication war is a disappointment, Napolitano said. It is a proceeding with exertion to shield our people groups from getting dependent on perilous medications. The U.S. government attempts this battle with the ass istance of taking an interest nations, for the most part from Latin America. The points of this crusade are a few. Right off the bat, the American War on Drugs plans to decrease illicit medication exchange. Also, they will likely battle radical political developments, mobs and revolts in different nations. The going with laws set out severe strategies and decisions so as to discourage the creation, conveyance and utilization of focused substances. (Grillo and Garcia, 2012; The White House.gov, n.d.) The United States attempted the War on Drugs during the Nixon organization and forty years on it is as yet seething. It is a very questionable activity by the United States on the worldwide unlawful medication exchange. The War on Drugs has been on for quite a while. What's more, many accept that it is being won as well. (Grillo and Garcia, 2012) The American war on drugs is viewed as a triumph since it is consistently achieving its objectives of dissuading unlawful medications from ente ring United States. Despite the fact that the demonstration despite everything occurs, the fringe watch security has been getting lawbreakers in the demonstration which are later attempted in the official courtroom. This has made many medication dealers proceed onward to various exchange as the peril and shame related with tranquilize transportation has expanded fundamentally. The medication exchange has numerous unsafe impacts on the wellbeing, wellbeing and security of the American residents. (The White House.gov, n.d.) U.S. what's more, Mexican law requirement authorities are of the assessment that the present flood of brutality in Mexico and other Latin American nations is because of the way that the war on drugs is making serious weights on the medication related associations and these come conflicting into one another. On the off chance that the medication exertion were falling flat there would be no brutality, a senior U.S. official said Wednesday. There is savagery in light of the fact that these folks are thrashing. We're taking these folks out. The most noticeably terrible thing you could do is stop now. (De-Cordoba) Drug clients put a colossal strain on society and cocaine related brutality is a case of what it does to sedate abusers and everyone around them. Hence, it is imperative to help the war on drugs. It might appear to be costly, yet the impact of medication abuser on our society’s wellbeing is considerably progressively exorbitant over the long haul. (Joined Nations, 1994) Compared to 30 years back, there has been a 46% abatement in cocaine use among youthful grown-ups in the previous five years. Another feature of this is the instruction program for adolescents and youthful grown-ups in which they are taught about the risks of medication misuse. Despite the fact that

5 Books That Anchor Me When Im Homesick

5 Books That Anchor Me When I’m Homesick This is a guest post from  Lynn Crothers. Lynn is a writer and editor bouncing between Minnesota and North Carolina. Wherever she is, she likes waking up real early in the morning to read. Say hi at awelcomingplace.com. ____________________ Last fall, I moved from my hometown in North Carolina to Minneapolis, a city I’d never visited before but was attracted to in part because of its healthy literary arts community. I did this on a whim because I craved change, but inevitably I found myself in the same familiar spot: missing home. Maybe other adventurous homebodies can relate? As I grow older, I grow wiser about how to live, but at many points in my life I’ve found myself in other states, cities, and countries for days, weeks, and years feeling pretty homesick. That’s not to say I haven’t loved these locations, just that I occasionally find myself longing places and things elsewhere. When this happens, getting out helps. Talking to friends and family. But over the years, when I’ve felt the most alone, it’s books that have provided the greatest comfort. Here are five I turn to again and again: 1. Tiny Beautiful Things by  Cheryl Strayed This book should be a part of everyone’s Emotional First Aid Kit. Cheryl Strayed is the tough, supportive, endlessly accepting mother/sister/friend. I don’t remember when I first read Tiny Beautiful Things, but it kinda comes with me everywhere now, like the Bible you find waiting in motel dresser drawers. I have a difficult time following other people’s advice, but when Strayed says “Let yourself be gutted. Let it open you. Start there,” I listen. 2. Sentimental, Heartbroken Rednecks by  Greg Bottoms I went to college in Vermont and loved it but often missed the South. Greg Bottoms is a fellow Southerner and also my former creative writing professor. I discovered this, one of his essay collections, after our class ended, and read it one summer while working at a hotel in New England. Sentimental, Heartbroken Rednecks not only introduced me to Breece D’J Pancake, it felt like reading a letter from an old friend, someone who gets what I’m saying before I say anything. Like Bottoms wrote, “I felt that largely irrational regional kinship Southerners […] expend so much energy talking about.” 3. Travels with Charley by  John Steinbeck Homesickness isn’t just about missing your literal home. Sometimes it’s about missing a sense of who you are. When I get caught up in stuff that doesn’t matter, I pull out my copy of Travels with Charley, which is marked up with pens, highlighters, and little neon flags. At its core, this is about a curious traveler who believed everyone had a story. “From start to finish,” Steinbeck wrote, “I found no strangers.” 4. A Tale for the Time Being by  Ruth Ozeki This is a new addition to my list, but an important one. I read A Tale for the Time Being when I was living in my hometown but still feeling homesick. What’s with that? Homesickness, maybe more than anything else, is a spiritual state that can’t be cured by a new location, a new job, a new apartment. It’s a matter of infusing meaning (and maybe meditation and a little hard work) into your life. Jiko taught me that. Who’s Jiko? “The thing about Jiko, one of her superpowers,” said 16-year-old Nao, our narrator, “is that just by being in the same room with you, she can make you feel okay about yourself. And it’s not just me. She does this with everyone. I’ve seen her.” 5.  Still Life With Woodpecker by Tom Robbins Last year I saw Tom Robbins speak at Malaprop’s Bookstore in Asheville, North Carolina. It felt like a dream, a long time coming. Robbins is a Southerner too, but that’s not what draws me to him. Still Life with Woodpecker helped form my definition of love, partnership, and the importance of playfulness. I read it many years ago. It was one of those books that arrived at the right time in my life. “Love is the ultimate outlaw,” Robbins wrote, “It just won’t adhere to any rules.” When I am homesick for a thing I can’t describe, these are the words I want to read again. ____________________ Celebrate National Library Week with our library lovers bundle for only $34!

Bowdoin College Acceptance Rate, SAT/ACT Scores

Bowdoin College is a private liberal arts college with an acceptance rate of 10.3%. Located near the coast in Brunswick, Maine, Bowdoin takes pride in both its beautiful location and its academic excellence.  Eight miles away from the main campus is Bowdoins 118-acre Coastal Studies Center on Orrs Island. Bowdoin was one of the first colleges in the country to move to a financial aid process that allows students to graduate without loan debt.   For its strong programs in the liberal arts and sciences, Bowdoin was awarded a chapter of the prestigious  Phi Beta Kappa  honor society. With its 9-to-1 student/faculty ratio and wide-ranging strengths, Bowdoin made our lists of top New England colleges and  top liberal arts colleges.   Considering applying to this highly selective school? Here are the Bowdoin College admissions statistics you should know. Acceptance Rate During the 2017-18 admissions cycle, Bowdoin College had an acceptance rate of 10.3%. This means that for every 100 students who applied, 10 students were admitted, making Bowdoins admissions process highly competitive. Admissions Statistics (2017-18) Number of Applicants 9,081 Percent Admitted 10.3% Percent Admitted Who Enrolled (Yield) 55% SAT Scores and Requirements Bowdoin has a test-optional standardized testing policy. Applicants to Bowdoin may submit SAT or ACT scores to the school, but they are not required. During the 2017-18 admissions cycle, 60% of admitted students submitted SAT scores. SAT Range (Admitted Students) Section 25th Percentile 75th Percentile ERW 650 740 Math 650 770 ERW=Evidence-Based Reading and Writing This admissions data tells us that of those who submitted test scores during the 2017-18 admissions cycle, most of Bowdoins admitted students fall within the  top 20% nationally  on the SAT. For the evidence-based reading and writing section, 50% of students admitted to Bowdoin scored between 650 and 740, while 25% scored below 650 and 25% scored above 740. On the math section, 50% of admitted students scored between 650 and 770, while 25% scored below 650 and 25% scored above 770. While the SAT is not required, this data tells us that a composite SAT score of 1510 or higher is a competitive score for Bowdoin College. Requirements Bowdoin does not require SAT scores for admission. For students who choose to submit scores, note that Bowdoin participates in the scorechoice program, meaning that the admissions office will consider your highest score from each individual section across all SAT test dates. Home-schooled applicants and those from high schools that dont assign grades will need to submit SAT or ACT test scores, including 2 or more SAT Subject tests. ACT Scores and Requirements Bowdoin College has a test-optional standardized testing policy. Applicants to Bowdoin may submit SAT or ACT scores to the school, but they are not required. During the 2017-18 admissions cycle, 46% of admitted students submitted ACT scores. ACT Scores (Admitted Students) Section 25th Percentile 75th Percentile English 32 35 Math 27 33 Composite 30 34 This admissions data tells us that of those students who submitted ACT scores to Bowdoin College, most fall within the  top 7% nationally  on the ACT. The middle 50% of students admitted to Bowdoin received a composite ACT score between 30 and 34, while 25% scored above 34 and 25% scored below 30. Requirements Bowdoin does not require ACT scores for admission. For students who choose to submit scores, note that Bowdoin participates in the scorechoice program, meaning that the admissions office will consider your highest score from each individual section across all ACT test dates. Home-schooled applicants and those from high schools that dont assign grades will need to submit SAT or ACT test scores, including 2 or more SAT Subject tests.. GPA Bowdoin College does not provide data about admitted students high school GPAs. Self-Reported GPA/SAT/ACT Graph Bowdoin College Applicants Self-Reported GPA/SAT/ACT Graph. Data courtesy of Cappex. The admissions data in the graph is self-reported by applicants to Bowdoin College. GPAs are unweighted. Find out how you compare to accepted students, see the real-time graph, and calculate your chances of getting in with a free Cappex account. Admissions Chances Bowdoin College, which accepts one tenth of applicants,  is a highly selective liberal arts college. Bowdoin uses a  holistic admissions  process which is based on much more than numbers. A strong  application essay  and glowing  letters of recommendation  can strengthen your application, as can participation in meaningful  extracurricular activities  and a  rigorous course schedule which includes AP, IB, Honors, and dual enrollment classes. In the graph above, the blue and green dots represent accepted students. Most had average high school GPAs in the A range (3.7 to 4.0) and combined SAT scores (ERWM) above 1300, but lower scores wont affect your chance of acceptance as the college has a test-optional admissions policy.  Applicants can choose whether to include their scores when they apply to Bowdoin. All admissions data has been sourced from the National Center for Education Statistics and Bowdoin College Undergraduate Admissions Office.

Silver-Spotted Skipper (Epargyreus clarus)

The silver-spotted skipper, Epargyreus clarus, frequents roadsides, fields, and backyard gardens throughout North America. Skippers dash quickly from flower to flower, as if they are skipping around the meadow. What Do Silver-Spotted Skippers Look Like? Chances are youve seen a silver-spotted skipper. With their brown wings and quick movement, they might not be the first butterflies youd stop to observe. Take a closer look, and youll notice bands of orange on the forewings, and a silvery patch in the center of the hindwings. The silver-spotted skipper is the largest skipper in North America, with a wingspan of 1 3/4 - 2 5/8 inches. Silver-spotted skippers have enormous eyes that appear to bulge out from the head. Epargyreus clarus also has short antennae with clubbed ends. The odd-looking caterpillar has an enlarged head capsule and a pronounced neck collar. With a deep rust or black head and two bright red eyespots in the front, the caterpillar appears quite like a cartoon alien from outer space. The larvas body is yellow-green, with thin dark lines running across its width. By some accounts, the silver-spotted skipper lays her eggs on plants near the host plant, but not on the actual host. This requires the newly hatched larva to crawl and locate its food source. Most experts seem to dispute this theory, and argue the butterfly lays directly on the host plant. How Are Silver-Spotted Skippers Classified? Kingdom - AnimaliaPhylum - ArthropodaClass - InsectaOrder - LepidopteraFamily - HesperiidaeGenus - EpargyreusSpecies - Epagyreus clarus What Do Silver-Spotted Skippers Eat? Larvae feed on legumes, especially woody legumes. Black locust is the favorite host plant. Other host plants include honey locust, false indigo, bush clover, and tick-trefoils. Adult silver-spotted skippers nectar on many flowers, but show a clear preference for blue, red, pink, or purple varieties. They rarely visit yellow flowers. The Silver-Spotted SkippersLife Cycle Like all butterflies, the silver-spotted skipper undergoes four stages during its life cycle, a complete metamorphosis. The generations per year vary by region, with southern populations having the most broods. Egg - Green, dome-shaped eggs are laid singly on upper side of leaves.Larva - The caterpillar has a large brown head, with red eyespots at the front. The body is a yellow-green color.Pupa - These skippers overwinter in the chrysalis, hidden in rolled leaf litter.Adult - Adults emerge in spring. Males perch on tall weeds or branches, watching for females. They also patrol for potential mates. Special Adaptations and Defenses ofSilver-Spotted Skippers At night, or when the daytime weather prohibits flight, silver-spotted skippers hang upside down under leaves. Caterpillars build themselves tiny shelters using carefully cut pieces of leaves. As they grow, they abandon their old homes and build larger ones by joining leaves with silk. Where DoSilver-Spotted Skippers Live? Open parks, fields, gardens, and meadows, and where larval food plants are available. In North America, the silver-spotted skipper is common from Mexico to southern Canada, with the exception of the Great Basin region and western Texas. Worldwide reports include sightings in parts of Europe, Asia, and Australia. Sources: Silver-spotted Skipper, Butterflies and Moths of North AmericaSilver-spotted Skipper, Massachusetts Audubon - Butterfly Atlas

Integration Free Essays

string(665) " com EXERCISE A 1\) 2\) 3\) 4\) 5\) 6\) 7\) 8\) x \? 2 x \? 10 x \? c 3 2 SPM QUESTIONS 1\) y \? x2 \? 2x \? 7 2\) y \? x3 \? 3 x 2 \? 10 3\) p \? 3, y \? x3 \? 2 x 2 \? 4 x4 \? x3 \? 3x \? c 2 4 3 1 x \? 4x \? \? c 3 x 4 2 x x 1 \? \? 3 \? 2x \? c 2 2 x 6 5 \? \? 2 x 2x 2 x 2 \? \?c 4 x 1 2 x3 \? 3 \? c x 2 x \? 2x \? c 2 ASSESSMENT 1\) \(a \) x 4 \? 3 2 x \? 2x \? c 2 2 3 \(b\) 3x \? \? 2 \? c x x 6 x 1 \(c \) \? \?c 9 24 x 4 x3 9 \(d \) \? 6x \? \? c 3 x y \? x4 \? 2 x2 \? 8 p\? 7 8 2 3 3 2 x \? x \? x 3 2 2 3 x \? 2 3 EXERCISE B 1\) y \? 3x 2 \? 2 x \? 1 3 x 2 24 \? 2 \? 2 2 x 2\) 2\) y \? 2 x 2 \? x \? 3 3\) y \? 3\) 4\) y\? 5\) y\? http://mathsmozac\." http://sahatmozac. blogspot. com ADDITIONAL MATHEMATICS FORM 5 MODULE 4 INTEGRATION http://mathsmozac. We will write a custom essay sample on Integration or any similar topic only for you Order Now blogspot. com http://sahatmozac. blogspot. com CHAPTER 3 : INTEGRATION Content Concept Map page 2 3–4 5 6 7 8–9 10 – 11 12 4. 1 Integration of Algebraic Functions Exercise A 4. 2 The Equation of a Curve from Functions of Gradients. Exercise B SPM Question Assessment Answer http://mathsmozac. blogspot. com 1 http://sahatmozac. blogspot. com Indefinite Integral a) o o a x n a dx = ax + c. xn+ 1 + c. n+ 1 b) x n dx = c ) o d x = a o x n d x = a n x + n + 1 1 + c . Integration of Algebraic Functions ) ) The [f (x)  ± g(x) ]dx = o f (x) dx  ± d o Equation of a Curve from Functions of Gradients o g(x)dx y = y = o f ‘( x ) d x c, f (x) + http://mathsmozac. blogspot. com 2 http://sahatmozac. blogspot. com INTEGRATION 1. Integration is the reverse process of differentiation. dy 2. If y is a function of x and = f ‘( x) then o f ‘( x)dx = y + c, c = constant. dx If dy = f ( x ), then dx o f ( x)dx = y 4. 1. Integration of Algebraic Functions Indefinit e Integral a) b) o o a dx = ax + c. n a and c are constants xn+ 1 x dx = + c. n+ 1 n c is constant, n is an integer and n ? – c) o ax dx = a o ax n + 1 x dx = + c. n+ 1 n and c are constants n is an d) o [f ( x )  ± g ( x ) ]dx = o f ( x) dx  ± o g ( x)dx http://mathsmozac. blogspot. com 3 http://sahatmozac. blogspot. com Find the indefinite integral for each of the following. a ) ? 5dx b) ? x 3 dx c) ? 2 x dx 5 d) ? ( x ? 3x 2 )dx Always remember to include ‘+c’ in your answers of indefinite integrals. Solution : a) ? 5dx ? 5x ? c b) 3 ? x dx ? x3? 1 ? c 3 ? 1 x4 = ? c 4 2 c) 5 ? 2 x dx ? 2 x5? 1 ? c 5 ? 1 2 x6 = ? c 6 1 = x6 ? c 3 d) ? ( x ? 3x )dx ? ? xdx ? ? 3x 2 dx = x 2 3 x3 ? ?c 2 3 x2 = ? x3 ? c 2 Find the indefinite integral for each of the following. a) ? ? x ? 3x ? dx 2 x 4 b) ?x ? x 2 4 ? ? ? 3 ? ? dx x ? ? a) Solution : x ? 3Ãâ€"2 ? ? x 4 ?dx ? ? x 3Ãâ€"2 ? ? ? x4 ? x4 ? dx ? ? b) 2 4? ? ? 2 4? ? 3 ? 4 ? dx = ? ? 3x ? 2 ? dx x ? x ? ? ? = ? 3à â€"2 ? 4 x ? 2 dx ? x ? 1 ? 3x 3 = ? 4? c 3 ? ?1 ? 4 = x3 ? ? c x ? ? x? 3 ? 3x? 2 dx ? x? 1 ? x? 2 = ? 3? c ? 2 ? ?1 ? 1 3 =? 2 ? ?c 2x x ? ? ? ? http://mathsmozac. blogspot. com 4 http://sahatmozac. blogspot. com 1. Find ? ? 3x 2 ? 4 x ? 10 dx. ? [3m] 2. Find ? ? x 2 ? 1 ? 2 x ? 3 ? dx. ? [3m] 1? ? 3. Find ? ? 2 x ? ? dx. x? ? 2 [3m] 4. Find ? ? 2x ? ? 3 ?x? 3 ? ? 2 ? dx. 4 x ? [3m] 6x ? 5 5. Integrate with respect to x. x3 [3m] 6. Find ? ?x 5 ? 4Ãâ€"2 2x 4 ? dx [3m] 3 ? ? 7. Find ? x ? 6 ? 6 ? x . x ? ? 2 [3m] 8. Integrate x 2 ? 3x ? 2 with respect to x. x ? 1 [3m] http://mathsmozac. blogspot. com 5 http://sahatmozac. blogspot. com The Equation of a Curve from Functions of Gradients dy ? f ‘( x), then the equation of the curve is dx If the gradient function of the curve is y ? ? f ‘( x ) dx c is constant. y ? f ( x) ? c, Find the equation of the curve that has the gradient function 3x ? 2 and passes through the point (2, ? 3). Solution The gradient function is 3x ? 2. dy ? 3x ? 2 dx y ? ? (3x ? 2)dx y? 3Ãâ€"2 ? 2x ? c 2 The curve passes through the point (2, ? 3). Thus, x = 2, y = ? 3. 3(2) 2 ? 3 ? ? 2x ? c 2 ? 3 ? 6 ? 4 ? c c ? 5 Hence, the equation of curve is y? 3x 2 ? 2x ? 5 2 http://mathsmozac. blogspot. com 6 http://sahatmozac. blogspot. com 1. Given that dy ? 6 x ? 2 , express y in terms of x if y = 9 when x = 2. dx 2. Given the gradient function of a curve is 4x ? 1. Find the equation of the curve if it passes through the point (? 1, 6). 3. The gradient function of a curve is given by dy 48 ? kx ? 3 , where k is a constant. dx x Given that the tangent to the curve at the point (-2, 14) is parallel to the x-axis, find the equation of the curve. http://mathsmozac. blogspot. com 7 http://sahatmozac. blogspot. com SPM 2003- Paper 2 :Question 3 (a) Given that y ? 2 x ? 2 and y = 6 when x = ? 1, find y in terms of x. dx [3 marks] SPM 2004- Paper 2 :Question 5(a) The gradient function of a curve which passes through A(1, ? 12) is 3 x 2 ? 6 x. Find the equation of the curve. [3 marks] http://mathsmozac. blogspot. com 8 http://sahatmozac. blogspot. com SPM 2005- Paper 2 :Question 2 A curve has a gradient function px 2 ? 4 x , where p is a constant. The tangent to the curve at the point (1, 3) is parallel to the straight line y + x ? 5 =0. Find (a) the value of p, [3 marks] (b) the equation of the curve. [3 marks] http://mathsmozac. blogspot. com 9 http://sahatmozac. blogspot. com 1. Find the indefinite integral for each of the following. (a) ? ? 4x 3 ? 3 x ? 2 dx ? (b) 3? x ? ? 2 2 ? 6? ? dx x3 ? 1 ? 2 ( c) (c) ? ? x 5 + 5 6x ? 3 ? ? dx ? ? x2 ? 3 (d) ? ? ? x2 ? ? ? 2 ? ? dx ? ? 2. If dy ? 4 x3 ? 4 x, and y = 0 when x = 2, find y in terms of x. dx http://mathsmozac. blogspot. com 10 http://sahatmozac. blogspot. com 3. If dp v3 ? 2v ? , and p = 0 when v = 0, find the value of p when v = 1. dv 2 4. Find the equation of the curve with gradient 2 x 2 ? 3 x ? 1, which passes through the origin. 5. d2y dy dy Given that ? 4 x, and that ? 0, y = 2 when x = 0. Find and y in terms 2 dx dx dx of x. http://mathsmozac. blogspot. om 11 http://sahatmozac. blogspot. com EXERCISE A 1) 2) 3) 4) 5) 6) 7) 8) x ? 2 x ? 10 x ? c 3 2 SPM QUESTIONS 1) y ? x2 ? 2x ? 7 2) y ? x3 ? 3 x 2 ? 10 3) p ? 3, y ? x3 ? 2 x 2 ? 4 x4 ? x3 ? 3x ? c 2 4 3 1 x ? 4x ? ? c 3 x 4 2 x x 1 ? ? 3 ? 2x ? c 2 2 x 6 5 ? ? 2 x 2x 2 x 2 ? ?c 4 x 1 2 x3 ? 3 ? c x 2 x ? 2x ? c 2 ASSESSMENT 1) (a ) x 4 ? 3 2 x ? 2 x ? c 2 2 3 (b) 3x ? ? 2 ? c x x 6 x 1 (c ) ? ?c 9 24 x 4 x3 9 (d ) ? 6x ? ? c 3 x y ? x4 ? 2 x2 ? 8 p? 7 8 2 3 3 2 x ? x ? x 3 2 2 3 x ? 2 3 EXERCISE B 1) y ? 3x 2 ? 2 x ? 1 3 x 2 24 ? 2 ? 2 2 x 2) 2) y ? 2 x 2 ? x ? 3 3) y ? 3) 4) y? 5) y? http://mathsmozac. You read "Integration" in category "Essay examples" blogspot. com 12 http://sahatmozac. logspot. com ADDITIONAL MATHEMATICS FORM 5 MODULE 5 INTEGRATION http://mathsmozac. blogspot. com 13 http://sahatmozac. blogspot. com CONTENT CONCEPT MAP INTEGRATION BY SUBSTITUTION DEFINITE INTEGRALS EXERCISE A EXERCISE B ASSESSMENT SPM QUESTIOS ANSWERS 2 3 5 6 7 8 9 10 http://mathsmozac. blogspot. com 14 http://sahatmozac. blogspot. com CONCEPT MAP INTEGRATION BY SUBSTITUTION un ? ax ? b ? dx ? ? du ? a n DEFINITE INTEGRALS If b d g(x) ? f (x) then dx b where u = ax + b, a and b are constants, n is an integer and n ? -1 OR (a) ? f (x)dx g(x)? ? g(b) ? g(a) a a (b) ? f (x)dx f (x)dx a a b b (c) ? f (x)dx f (x)dx ? ? f (x)dx a b a b c ? a x ? b ? ? ? ax ? b ? dx ? a ? n ? 1? n n ? 1 ? c, where a, b, and c are constants, n is integer and n ? -1 http://mathsmozac. blogspot. com 15 http://sahatmozac. blogspot. com INTEGRATION BY SUBSTITUTION un ? ? ax ? b ? dx ? ? a du n where u = ax + b, a and b are constants, n is an integer and n ? -1 O R ? ax ? b ? ? ? ax ? b ? dx ? a ? n ? 1? n n ? 1 ? c, where a, b, and c are constants, n is integer and n ? -1 Find the indefinite integral for each of the following. (a) ? ? 2 x ? 1? dx 3 (b) ? 4(3 x ? 5)7 dx 2 (c) ? dx (5 x ? 3)3 SOLUTION (a) ? ? 2 x ? 1? dx 3 Let u = 2x +1 du du ? 2 ? dx ? dx 2 3 3 ? du ? ? (2 x ? 1) dx ? ? u ? ? ? ? u3 = ? du 2 u 3 ? 1 = ? c 2(3 ? 1) u4 +c 8 (2 x ? 1) = +c 8 = Substitute 2x+1 and substitute dx with du dx = 2 OR (2 x ? 1) 4 ? c ? (2 x ? 1) dx ? 2(4) 3 = ? 2 x ? 1? 8 4 ?c Substitute u = 2x +1 http://mathsmozac. blogspot. com 16 http://sahatmozac. blogspot. com (b) ? 4(3 x ? 5) dx 7 (c) Let u ? 3 x ? 5 du du ? 3 ? dx ? dx 3 7 4u 7 du ? 4(3 x ? 5) dx ? ? 3 4u 8 = ? c 3(8) u8 ? c 6 (3u ? 5)8 = ? c 6 = 2 dx ? ? 2(5 x ? 3) ? 3 dx (5 x ? 3)3 Let u ? 5 x ? 3 du du ? 5 ? dx ? dx 5 ? 3 2u ? 3 du ? 2(5 x ? 3) dx ? ? 5 2u ? 3 = ? c 5(? 2) ? OR 4(3 x ? 5)8 ? c ? 4(3 x ? 5) dx ? 3(8) 7 u ? 2 ? c ? 5 1 = ? 2 5u 1 =? ?c 5(5 x ? 3)2 = = (3x ? 5)8 ? 6 DEFINITE INTEGRALS If d g ( x) ? f ( x) then dx b (a) (b) ? b a b f ( x)dx ? ? g ( x) ? ? g (b) ? g (a) a ? (c ) ? a b f ( x)dx ? ? ? f ( x)dx a b a f ( x)dx ? ? f ( x)dx ? ? f ( x)dx b a c c http://mathsmozac. blogspot. com 17 http://sahatmozac. blogspot. com Evaluate each of the following ( x ? 3)( x ? 3) (a) ? 12 dx x4 1 1 (b) ? 0 dx (2 x ? 1) 2 SOLUTION (a) x2 ? 9 2 ( x ? 3)( x ? 3) ? c ? ?12 4 dx ? 1 x4 x 2 9 ? 2? x = ? 1 ? 4 ? 4 ? dx x ? ?x = ? 12 ( x ? 2 ? 9 x ? 4 )dx ? x ? 1 ? x ? 3 ? ? =? ? 9? ? ? 3 ? ?1 ? ?1 2 2 (b) ?0 1 1 1 dx ? ?0 (2 x ? 1)? 2 dx 2 (2 x ? 1) 1 = ? 0 (2 x ? 1) ? 2 dx ? (2 x ? 1) ? 1 ? =? ? ? ?1(2) ? 0 ? 1 = ? ? 2(2 x ? 1) ? 0 =? ? ? 1 1 ? 2[2(1) ? 1] ? 2[2(0) ? 1] ? 1 1 ? 1 3? = ? 3 ? ? x x ? 1 ? 1 3 ? ? 1 3? = ? 3 ? ? 3 ? ? 2 2 ? ? 1 1 ? 1 3 = ? ? ? (? 1 ? 3) 2 8 1 =? ?2 8 1 =? 2 8 1 ? 1? = ? ? 6 ? 2? 1 = 3 http://mathsmozac. blogspot. com 18 Distributed:18. 1. 09 Return:20. 1. 09 INTEGRATE THE FOLLOWING USING SUBSTITUTION METHOD. (1) ? ( x ? 1)3dx (2) ? ?4 ? 3 x ? 5 ? dx ? 5 (3) ? 1 ? 5 x ? 3? dx 4 1 ? ? (4) ? ? 5 ? x ? dx 2 ? ? ?3 1 ? ? (5) ? 5 ? 4 ? y ? dy 2 ? ? 4 3? 2 ? (6) ? ? 5 ? u ? du 2? 3 ? 5 19 http://sahatmozac. blogspot. com EXERCISE B 8 1. Evaluate ? 3 ( x3 ? 4)dx Answer : 1023. 75 2. Evaluate Answer: 3 ? ?3 1 2 x( x ? x ? 5)dx 8 83 96 ?2 ? 3. Integrate ? x ? 5 ? with respect to x ? 3 ? 4 4. Evaluate ? 1 3 1 ? ? ? 2 ? 3x ? 4 ? dx ? 1 x ? ? 1 Answer: 3 ? 2 ? ? x ? 5? ? c 10 ? 3 ? 5 Answer : 3 5. Evaluate ? 3 1 ? 2 x ? 1 2 x ? 1? dx 4 x2 6. Given that of 2 5 ? 5 2 f ( x)dx ? 10 , find the value 5 Answer: 1 6 ? ? 1 ? 2 f ( x)? dx Answer :17 http://mathsmozac. blogspot. com 20 http://sahatmozac. blogspot. com ASSESSMENT ?6 and 2. (a) ? 5(2 ? 3v) dv 4 (b) ? dx 5 3 ? 1 ? 5 x ? 1. Given that ? 2 2 1 f ( x)dx ? 3 ? 2 3 f ( x)dx ? ?7 . Find (a) the value of k if (b) ? ? kx ? f ( x)? dx ? 8 1 ? ? 5 f ( x) ? 1? dx 3 1 Answer : (a) k = (b) 48 22 3 3. Show that d ? x 2 ? 2 x 2 ? 6 x 4. . ? dx ? 3 ? 2 x ? ? 3 ? 2 x ? 2 4 Given that ? 4 0 f ( x)dx ? 3 and Hence, find the value of Answer : 1 10 ? ? 3 ? 2x ? 0 1 x ? x ? 3? ? 0 g ( x)dx ? 5 . Find 4 0 2 dx . ? f ( x)dx ? ? g ( x)dx (b) ? ?3 f ( x) ? g ( x)? dx (a) 0 4 0 4 Answer: (a) – 15 (b) 4 http://mathsmozac. blogspot. com 21 http://sahatmozac. blogspot. com SPM QUESTIONS SPM 2003 – PAPER 1, QUESTION 17 1. Given that ? SPM 2004 – PAPER 1, QUESTION 22 k n dx ? k ? 1 ? x ? ? c , 2. Given that 1 ? 2 x ? 3? dx ? 6 , where k ; -1 , find the value of k. [4 marks] ? 1 ? x ? find the value of k and n [3 marks] Answer: k = 5 5 Answer: k = ? =-3 3 5 4 SPM 2005 – PAPER 1, QUESTION 21 6 6 3. Given that ? 2 f ( x)dx ? 7 and ? 2 (2 f ( x) ? kx)dx ? 10 , find the value of k. Answer: k = 1 4 http://mathsmozac. blogspot. com 22 http://sahatmozac. blogspot. com ANSWERS EXERCISE A 1. 3 ( x + 1)4 + c 2. 60 (3 x +5) – 4 + c 3. ?20 EXERCISE B 1. 1023. 75 ? 5 x ? 3? 3 ?c 2. 3 83 96 5 4. 3? 1 ? ?5 ? x? ? c 2? 2 ? ? y? ?c ? 6 4 ?2 3 ? 2 ? 3. ? x ? 5? ? c 10 ? 3 ? 1 3 5 5. 1 6 6. 17 1 ? 5. ?10 ? 4 ? 2 ? 6. 4. 3 2 ? ? ? 5 ? 5 ? u ? ? c 3 ? ? ASSESSMENT 22 1. (a) k = 3 (b) 48 2. (a) 90(2 – 3v) +c ? 100 (b) (1 ? 5 x) ? 4 ? c 3 3. 1 10 -5 SPM QUESTIONS 1. k = ? 2. k = 5 3. = 1 4 5 3 n=-3 4. (a) – 15 (b) 4 http://mathsmozac. blogspot. com 23 http://sahatmozac. blogspot. com ADDITIONAL MATHEMATICS MODULE 6 INTEGRATION http://mathsmozac. blogspot. com 24 http://sahatmozac. blogspot. com CHAPTER 3 : INTEGRATION Content Concept Map 9. 1 Integration as Summation of Areas page 2 3 4–6 7–8 9 – 11 12 – 14 15 Exercise A 9. 2 Integration as Summation of Volumes Exercise B SPM Question Answer http://mathsmozac. blogspot. com 25 http://sahatmozac. blogspot. com a) The area under a curve which enclosed by x-axis, x = a and x = b is a) The volume generated when a curve is rotated through 360? bout the x-axis is ? ? b a y dx b ) The area under a curve which enclosed by y-axis, y = a and y = b is b a Vx ? ? ? y 2 dx a b x dy b) The volume generated when a curve is rotated through 360? about the y-axis is c) The area enclosed by a curve and a straight line ? ? f ( x) ? g ( x)? dx b a Vy ? ? ? x 2 dy a b http://mathsmozac. blogspot. com 26 http://sahatmozac. blogspot. com 3. INTEGRATION 3. 1 Integration as Summation of Area y y = f(x) b a a b 0 The area under a curve which enclosed by x = a and x = b is x 0 x y = f(x) ? b a ydx The area under a curve which is enclosed by y = a and y = b is Note : The area is preceded by a negative sign if the region lies below the x – axis. ? b a xdy Note : The area is preceded by a negative sign if the region is to the left of the y – axis. The area enclosed by a curve and a straight line y y = g (x) y = f (x) a The area of the shaded region = = b b x ? ? ? f ( x) ? g ( x)? dx a b a a b f ( x)dx ? ? g ( x) http://mathsmozac. blogspot. com 27 http://sahatmozac. blogspot. com 1. Find the area of the shaded region in the diagram. y y = x2 – 2x 2. Find the area of the shaded region in the diagram. y y = -x2 + 3x+ 4 x -1 0 4 0 x http://mathsmozac. blogspot. com 28 http://sahatmozac. logspot. com 3. Find the area of the shaded region y y=2 4. Find the area of the shaded region in the diagram. y y = x2 + 4x + 4 0 x = y2 x -2 -1 0 2 x http://mathsmozac. blogspot. com 29 http://sahatmozac. blogspot. com 5. Find the area of the shaded region in the diagram y 1 x = y3 – y x 6. y y = ( x – 1)2 0 0 x x=k -1 Given that the area of the shaded region in 28 the diagram above is units2. Find the 3 value of k. http://mathsmozac. blogspot. com 30 http://sahatmozac. blogspot. com 3. 2 Integration as Summation of Volumes y y=f(x) The volume generated when a curve is rotated through 360? about the x-axis is 0 a b x Vx ? ? ? y 2 dx a b y y=f(x) The volume generated when a curve is rotated through 360? about the y-axis is b a 0 x Vy ? ? ? x 2 dy a b http://mathsmozac. blogspot. com 31 http://sahatmozac. blogspot. com y y=x(x+1) Find the volume generated when the shaded region is rotated through 360? about the x-axis. x 0 Answer : x=2 ? ? ? y 2 dx 0 2 Volume generated ? ? ? x 2 ? x ? 1? dx 2 2 0 ? ? ? ( x 4 ? 2 x3 ? x 2 )dx 0 2 ? x 5 2 x 4 x3 ? ? ? ? ? 4 3 ? 0 ? 5 2 25 2(2)4 23 ? ? ? ? ? ? ? ? 0? 5 4 3? ? 256 1 ? ? @ 17 ? units 3 . 15 15 y y ? 6 ? x2 The figure shows the shaded region that is enclosed by the curve y ? ? x 2 , the x-axis and the y-axis. Calculate the volume generated when the shaded region is revolved through 360? about y-axis. 0 Answer : Given y ? 6 ? x 2 substitute x ? 0 into y ? 6 ? x Then, y ? 6? 0 y? 6 2 x Volume generated ? ? ? x 2 dy 0 6 ? ? ? ? 6 ? y ? dx 6 0 ? y2 ? ? ? ?6 y ? ? 2 ? 0 ? 62 ? ? 6(6) ? 2 ? 18? units 3 . ? ? ? ? 0? ? ? 6 http://mathsmozac. blogspot. com 32 http://sahatmozac. blogspot. com 1. y y = x (2 – x) 0 x The above figure shows the shaded region that is enclosed by the curve y = x (2 – x) and x-axis. Calculate the volume generated when the shaded region is revolved through 360? bout the y-axis. [4 marks] http://mathsmozac. blogspot. com 33 http://sahatmozac. blogspot. com 2. y R (0, 4) Q (3, 4) P (0, 2) y? = 4 (x + 1) 0 x=3 x The figure shows the curve y ? ( x ? 2) 2 . Calculate the volume generated when the shaded region is revolved through 360? about the x-axis. http://mathsmozac. blogspot. com 34 http://sahatmozac. blogspot. com 3. y R (0, 4) x y ? ? 3? x 0 x=k The above figure shows part of the curve y ? ? 3 ? x and the straight line x = k. If the volume generated when the shaded region is revolved through 1 360? about the x-axis is 12 ? units3 , find the value of k. 2 http://mathsmozac. logspot. com 35 http://sahatmozac. blogspot. com SPM 2003- Paper 2 :Question 9 (b) Diagram 3 shows a curve x ? y 2 ? 1 wh ich intersects the straight line 3 y ? 2 x at point A. y 3 y ? 2x 3y ? 2x x ? y2 ? 1 ?1 0 x Diagram 3 Calculate the volume generated when the shaded region is involved 360? about the y-axis. [6 marks] http://mathsmozac. blogspot. com 36 http://sahatmozac. blogspot. com SPM 2004- Paper 2 :Question 10 Diagram 5 shows part of the curve y ? y 3 ? 2 x ? 1? 2 which passes through A(1, 3). A(1,3) y? 0 a) b) Diagram 5 3 ? 2 x ? 1? 2 x Find the equation of the tangent to the curve at the point A. [4 marks] A egion is bounded by the curve, the x-axis and the straight lines x=2 and x= 3. i) Find the area of the region. ii) The region is revolved through 360? about the x-axis. Find the volume generated, in terms of ? . [6 marks] http://mathsmozac. blogspot. com 37 http://sahatmozac. blogspot. com SPM 2005- Paper 2 :Question 10 In Diagram 4, the straight line PQ is normal to the curve y ? straight line AR is parallel to the y-axis. y x2 ? 1 at A(2, 3). The 2 y? x2 ? 1 2 A(2, 3) 0 R Diagram 4 Fin d (a) (b) (c) Q(k, 0) x the value of k, [3 marks] the area of the shaded region, [4 marks] the volume generated, in terms of ? when the region bounded by the curve, the y-axis and the straight line y = 3 is revolved through 360? about y-axis. [3 marks] http://mathsmozac. blogspot. com 38 http://sahatmozac. blogspot. com EXERCISE A EXERCISE B 1. 1 1 ? unit 2 15 1. 1 1 units 2 3 5 units 2 6 2. 2. 20 3 6 ? unit 3 5 k ? ?2 3. 3. 2 2 units 2 3 2 units 2 3 SPM QUESTIONS SPM 2003 Volume Generated ? 52 ? units3 15 4. 24 SPM 2004 i) Area ? 1 units 2 5 49 ? units3 1125 5. 1 units 2 2 k? 4 ii) Volume Generated ? 6. SPM 2005 a) k ? 8 1 b) Area ? 12 units2 3 c) Volume Generated ? 4? units? http://mathsmozac. blogspot. com 39 How to cite Integration, Essay examples

Chinese Sports and the Values of Taoism and Confucianism free essay sample

This paper reviews the book Training the Body for China by Brownell, which presents the practices, objects and activities of Chinese sports and material arts. This paper discusses that, unlike Western sports, Chinese sports and martial art are developed based on religious beliefs; in China, sports are based on two native religions, Taoism and Confucianism. The author reviews Susan Brownells Training the Body for China in which she shares her studies of Chinese Olympic sports and martial arts. For example, the author point out that, in sport, Chinese culture employs self-disciplinary actions to deal with misbehavior to sustain order, a value of Confucianism. One of the beliefs Confucianism values is the importance of family; this notion is also the linkage between Confucianism and the practices Chinese sports. One of ethical lessons Confucianism teaches is Hsiao, which signifies love within family; this notion is also apparent in Chinese sports. According to Brownell, there has been a phenomenon of developing family-funded sports clubs and village-based associations among Chinese. We will write a custom essay sample on Chinese Sports and the Values of Taoism and Confucianism or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Having family-funded sport clubs consisting family members as players clearly indicates how Confucianism value has become a part of Chinese life and sports.