Key concepts of calculus Essay Example | Topics and Well Written Essays - 500 words

Key concepts of calculus - Essay Example It is basically the instaneous rate of change of f(x) with respect to x. Graphically, this is analogous to the formula for gradient that we studied in earlier classes that is . This is basically the gradient of the tangent line to the curve traced by the function. 5. An absolute maximum value is one which is greater than all other values of f(x) for all values of x. This means there is an absolute maximum at if for all values of x. A local maximum is one which is greatest value of f(x) within a given range of x. This means 6. is basically a summation of products of countless small rectangles which form a shape on a graph. Here, is analogous to the area of a rectangle where. The only difference is that as f(x) is traced along the graph, its height changes. The number n represents the total number of rectangles made and since it approaches infinity, it means that there width grows shorter and shorter and the whole sum effectively gives the area under the curve with minimum shoot over. The main difference between definite and indefinite integral in this context is that the former has a defined domain for which this area is being calculated while the latter has domain equivalent to all real numbers. Definite integral represents area bounded by x axis, the curve and the two vertical lines at limits of domain. Indefinite integral may or may not be bounded from right or left and also, the height of curve is also unknown. So the height of rectangles is also unknown. 7. For the definite integral, bounded below by and above by , of a function, the derivative is the value of function at and the limit is the proof of its continuity. This is true regardless of the value of

Global Demographics Essay Example | Topics and Well Written Essays - 750 words

Global Demographics - Essay Example Companies in the business of entertainment will need to pay far greater attention to Spanish speaking Americans in their product offering than they needed to a few years ago, as Hispanics are the fastest growing ethnic group. Products and services geared toward working mothers are very likely to enjoy success in an atmosphere in which women are pursuing careers before and after having children. Businesses that are blind to these kinds of demographic trends are likely to stagnate and ultimately lose out to more astute competitors. In an environment of global growth and diversity, there are trends that are likely to pose great challenges to competition and business success. The ability of an organization to embrace diversity and leverage it to strengthen its products and services, as well as its community image, is crucial to the ongoing success and competitiveness of any business today. No longer can businesses make assumptions of homogeneity in any market in which they choose to operate. Multiculturalism and diversity have redefined everything from what it means to be American or European to what is considered a family. Organizations must prepare to meet the ch... Question 3 If diversity could be viewed as a business strategy, it most certainly would contribute to an organization's competitive advantage. Communities are becoming ever more diversified; and organizations that fail to acknowledge and respond to that growing diversity risk becoming out of touch with the market in which they seek to operate successfully. Successful business have their finger on the pulse of what is going on in the market place, and are able to change and adapt accordingly. Those that remain stodgy and inflexible in the way they operate, and the way they develop and market their products and services, in the face of a demographically dynamic marketplace are very likely to be left out in the cold. A business strategy of diversity means utilizing market intelligence to quickly detect and respond to demographic and other changes in the market. It means relating to a diverse market by cultivating an image of diversity through public relations efforts, and committing to products and services that resonate with a diverse clientele. Those organizations that pursue this type of business strategy will enjoy a strong competitive market position well into the future. Question 4 Trends in changing demographics and global business expectations that demand attention from organizations desiring to remain competitive in the future include populations that are aging, becoming more ethnically diverse, and have greater access to information than ever before. People today have the ability to virtually instantaneously retrieve information about their product options, facts about the competition, and communication with others with