Continuity and Differentiability Extra questions: 1) If f(x) = is continuous at x = 0‚ find the value of a and b 2) A function f is defined as f(x) = for x 1 = - for x = 1. Show that f(x) is differentiable at x = 1 and find its value 3) Let f(x) = if x 2 = k‚ if x = 2. If f(x) is continuous for all x‚ then find the value of k. 4) Let f(x) be a function of x defined as f(x) = ‚ x 1
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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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almost every thriving civilization has relied heavily on trade. Trading methods‚ groups‚ and technology has evolved through the centuries. A perfect example of this is Eurasia from 600-1450. There were many continuities and changes in Eurasian trade. During this time period there was continuity with how trade spread ideas and disease‚ but there was also change in technology that allowed trading over larger distances and in who controlled trade. Much of how trade spread ideas and disease
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THE CONTINUITY OF PARKS BY JULIO CORTÁZAR H E HAD BEGUN TO READ THE NOVEL a few days before. He had put it aside because of some urgent business‚ opened it again on his way back to the estate by train; he allowed himself a slowly growing interest in the plot‚ in the drawing of characters. That afternoon‚ after writing a letter to his agent and discussing with the manager of his estate a matter of joint ownership‚ he returned to the book in the tranquility of his study which looked
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Seventy four years since its founding‚ Toyota Motor is almost at the pinnacle of the global auto industry‚ having overtaken Ford Motor and General Motors in vehicle sales. Toyota was established in 1937 in Japan. Toyota has grown from being a small Japanese carmaker in the 1960s to the biggest carmaker in 2007‚ outranking General Motors. The founding principles for this success were embodies by the “Toyota Way” – a respect for learning‚ truth‚ trust‚ team-work‚ challenge and continuous improvement
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Chapter 2 Types of Innovation LEARNING OBJECTIVES When you have completed this chapter you will be able to: • Distinguish the different forms that innovation can take‚ such as product‚ process and service innovation • Differentiate and distinguish between the different types of innovation‚ such as radical and incremental innovation • • Describe each type of innovation Analyse different types of innovation in terms of their impact on human behaviour‚ business activity and society
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Continuity of care is defined as the continuation of care of a patient over time by multiple health care providers (REF 1). Continuum of care is defined as care of a patient over time from preventive medicine to early intervention to acute care‚ through rehabilitation‚ from the hospital to the home‚ and involving community services and medical and social aspects of care (Ref 2). Continuity of care is multidimensional and has been used to describe many different relationships between health care
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cost as generic strategies to try and gain a competitive advantage over their competitors in the automotive industry. The market scope that Toyota uses is a broad one that encompasses nearly every type of customer that is in the market to purchase an automobile. Toyota is able to target such a large market because they have something for everyone. Toyota has four wheel drive trucks and SUVs for the outdoor types or those who live in areas that face severe weather conditions‚ hybrid models like
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Toyota Production System Basics What are the main pillars of TPS? 1. Standardization 2. Just in Time Manufacturing 3. Lean Kaizen 4. Jidoka or Autonomation 5. Total Productive Maintenance TPS Objectives Reduce cost by the elimination of waste- good products that are safer and lower in cost. Make it easier to obtain and guarantee good quality. Based on teamwork and respect for human life‚ create a workplace where all can fulfill their potential. Build a lean production
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Toyota and GM: a Comparison of its Mission‚ Values‚ Social Responsibility‚ and Ethics Toyot Toyota and GM: a Comparison of its Mission‚ Values‚ Social Responsibility‚ and Ethics Toyota and General Motors are both in the manufacturing and sale of motor vehicles. They each have its own mission‚ values and conscientious effort to be socially responsible. A company’s mission‚ vision and core values define how the corporation functions and interacts with the local and global community. Corporations
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