Creating a scoring rubric

Analytical Scoring Rubric 1=unsatisfactory 2=Minimal competence 3=competent 4=exemplaryAdvertising We will write a custom essay sample on Creating a scoring rubric specifically for you for only $16.05 $11/page Learn More Scoring rubric for social science essay assignment Aspects Criteria (Descriptions of Scoring Levels) Score Editorial Aspect 1: Clarity, organization, word usage, and understandability Student has shown no evidence of clarity, organization, word usage and ease of understanding. Articulation of response is poor Response articulation is not detailed. There is limited evidence of clarity, organization, usage of words, and understandability Response articulation is plausible. The candidate has shown competency in clarity, organization, word usage, and understandability of paper Response articulation is competent. The candidate has shown high competency in clarity, organization, word usage, and understandability of paper Editorial Aspect 2: Grammar punctuation and spelling The student’s work has numerous grammar, punctuation and spelling mistakes that interfere with the flow and meaning of essay. The student’s work contains major grammar, punctuation and spelling mistakes that disrupt the flow and clarity of response The student’s contains no grammar, punctuation and spelling mistakes but has a few detectable minor mistakes The student’s work has no grammar, punctuation and spelling mistakes that are readily detectable therefore the response is meaningful and clear Editorial Aspect 3: Paper quality Student’s paper is completely substandard with no quality Incompetence in writing and research skills The student provides sufficient logical explanation of the five required point of view. The student displays paper of high quality with no errors. Student show impressive understanding of the topic Editorial Asp ect 4: Introduction and conclusion The student fails to provide a logical conclusion that summarizes the five required points of view The student provides an insufficient summary of the main points. The conclusion is generally weak and does not explain much The student provides sufficient summary of the main points. The conclusion is generally strong but too short with few details The student provides sufficient and well articulated summary of the main points. The conclusion is strong and does not leave out any detail of the discussion Content Aspect 1: Five different point of view: slavery, nationalism sectionalism, territorial crisis, and state rights The student fails to provide a description and comparison of any point of view as to why the US civil war occurred. There is no clear evidence of the relevance in the student’s discussions The student clearly provides only two of the five required point views as to why the US Civil War occurre d. There is limited evidence of relevance of discussion The student only provides at least four of the five required point of view as to why the US Civil War occurred, and compares and contrast them properly to create a relevant discussion The student provides all of the five required point of view as to why the US Civil War occurred, and compares and contrast them properly to create a relevant discussion. Content Aspect 2: comparing critical aspects The student fails to provide a description and comparison of any point of view as to why the US civil war occurred. There is no clear evidence of the relevance in the student’s discussions The student clearly provides only two of the five required point views as to why the US Civil War occurred. There is limited evidence of relevance of discussion The student only provides at least four of the five required point of view as to why the US Civil War occurred, and compares and contrast them properly to create a relevant discussion The student provides all of the five required point of view as to why the US Civil War occurred, and compares and contrast them properly to create a relevant discussion. Content Aspect 3: Depth of research The student fails to provide a logical explanation of the five required point of view. The student only mentions a few of the points with no logic detail information about the issues The student provides a logical explanation of the five required point of view but with minimal competency. The student only mentions a few of the points with no logical detail information about the issues The student provides sufficient logical explanation of the five required point of view. The student mentions at least all of the points with no logic detail information about the issues The student provides sufficient logical explanation of the five required point of view. The student mentions at least all of the points with logic detail in formation about the issues Content Aspect 4: in-text citation and references The student fails to use 3 primary and 2 secondary sources or fails to include any in-text citation or references for the primary and secondary sources used The student only provides at least two in-text citation for the required number of sources The student uses five sources ( three primary and two secondary sources) and gives appropriate references and in-text citation but with formatting errors based on APA standards The student uses five sources ( three primary and two secondary sources) and gives appropriate references and in-text citation but with no formatting errors based on APA standards Level of performance Unsatisfactory The lowest level of performance is unsatisfactory. This level gets a score of 1. Generally, a candidate who gets this score did not understand the assignment in any way (Tierney and Marielle, 2004). There is an obvious lack of understanding of what is required. Both editorial and content aspects are poorly displayed (Tierney and Marielle, 2004). Clearly, the student did not take time to do the assignment well. Minimal competence This is the second lowest level of performance. Student’s work in this level has a few major mistakes and other minor mistakes (Tierney and Marielle, 2004). The student shows inadequate understanding of the assignment. The logic of argument also lacks clarity making it hard for the reader to understand (Tierney and Marielle, 2004). Basically the student failed to take time to do the assignment and therefore was forced to do it in a rush (Tierney and Marielle, 2004). Competent This level of performance is good and satisfactory. The student will show an understanding of all aspects needed to be measured. There are no major mistakes but there can be a few detectable minor mistakes (Mertler, 2001). Exemplary This is the highest level of performance. The student shows high competence of understand an d responding to the assignment (Moskal, 2000). The work is free of major and minor errors. This level shows that student spent quality time to research and do the assignment (Moskal, 2000). References Mertler, C. 2001, ‘Designing scoring rubrics for your classroom’, Practical assessment,  research and evaluation, vol. 7, no. 2, Viewed on https://pareonline.net/getvn.asp?v=7n=25Advertising Looking for essay on education? Let's see if we can help you! Get your first paper with 15% OFF Learn More Moskal, B. 2000, ‘Scoring Rubrics: What, when and how?’, Practical assessment  research and evaluation, vol. 7, no. 3, Viewed on https://pareonline.net/getvn.asp?v=7n=3 Tierney, R. Marielle, S. 2004, ‘What’s still wrong with rubrics: focusing on the consistency of performance criteria across scale levels‘, Practical assessment research and evaluation, vol. 9, no. 2, Viewed on https://pareonline.net/getvn.asp?v=9n=2 This essay on Creating a scoring rubric was written and submitted by user Ignacio Lindsay to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Mangrove Habitat Profile

Mangrove Habitat Profile Their unusual, dangling roots make mangroves look like trees on stilts. The term mangrove can be used to refer to certain species of trees or shrubs, a habitat or a swamp. This article focuses on the definition of mangroves and mangrove swamps, where mangroves are located and marine species you can find in mangroves.   What Is a Mangrove? Mangrove plants are halophytic (salt-tolerant) plant species, of which there are more than 12 families and 80 species worldwide. A collection of mangrove trees in an area makes up a mangrove habitat, mangrove swamp or mangrove forest.   Mangrove trees have a tangle of roots which are often exposed above water, leading to the nickname â€Å"walking trees.† Where Are Mangrove Swamps? Mangrove trees grow in  intertidal  or estuarine areas. They are found in warmer areas between the latitudes of 32 degrees north and 38 degrees south, as they need to live in areas where the average annual temperature is above 66 degrees Fahrenheit. It is thought that mangroves were originally found in southeast Asia, but have been disbursed around the world and are now found  along the tropical and subtropical coasts of Africa, Australia, Asia, and North and South America.  In the U.S., mangroves are commonly found in Florida. Mangrove Adaptations The roots of mangrove plants are  adapted  to filter salt water, and their leaves can excrete salt, allowing them to survive where other land plants cannot. Leaves that fall off the trees provide food for inhabitants and breakdown to provide nutrients to the habitat.   Why Are Mangroves Important? Mangroves are an important habitat. These areas provide food, shelter and nursery areas for fish, birds, crustaceans and other marine life. They also provide a source of livelihood for many humans around the world, including wood for fuel, charcoal and timber and areas for fishing. Mangroves also form a buffer that defends coastlines from flooding and erosion. What Marine Life Are Found in Mangroves? Many types of marine and terrestrial life utilize mangroves. Animals inhabit the mangrove’s leafy canopy and waters underneath the mangrove’s root system and live in nearby tidal waters and mudflats. In the U.S., larger species found in mangroves include reptiles such as the American crocodile and American alligator; sea turtles including the hawksbill, Ridley, green and loggerhead; fish such as snapper, tarpon, jack, sheepshead, and red drum; crustaceans such as shrimp and crabs; and coastal and migratory birds such as pelicans, spoonbills and bald eagles. In addition, less-visible species such as insects and crustaceans live among the roots and branches of the mangrove plants. Threats to Mangroves: Natural threats to mangroves include hurricanes, root clogging from increased water turbidity, and damage from boring organisms and parasites.Human impacts on mangroves have been severe in some places, and include dredging, filling, diking, oil spills, and runoff of human waste and herbicides. Some coastal development results in total loss of habitat. Conservation of mangroves is important for the survival of mangrove species, humans and also for the survival of two other habitats – coral reefs and seagrass beds. References and Further Information: American Museum of Natural History. What Is a Mangrove? And How Does it Work?. Accessed June 30, 2015.Coulombe, D. A. 1984. The Seaside Naturalist. Simon Schuster. 246pp.Law, Beverly E. and Nancy P. Arny. â€Å"Mangroves-Florida’s Coastal Trees†. University of Florida Cooperative Extension Service. Retrieved online October 17, 2008 (as of August 2010, the document appears to no longer be online).

Economic growth Assignment Example | Topics and Well Written Essays - 250 words

Economic growth - Assignment Example Viele Accounting. Pg 224-225, Question p6 a) Truck 28200 Notes Payable 28200 b) Truck 28200 Capital lease liability (4.6229 * 6100) 28200 Depreciation Expense 4700 Accumulated Depreciation 4700 c) Interest Expense 2256 Capital Lease Liability 3844 Cash 6100 d) The expenses for the first year are Interest Expense and Depreciation = 2256 + 4700 = $6956 Somers and Seville. Exploration 8. Chapter 6 pg 118. a) 67.38 is the population in our base year 1980. We are considering the growth rate from this year which is around 102% or 1.206. This shows the rate of increase in population each year from 1980. b) 67.38. (1.206)^10 = 438.53 Million. McConnell and Brue pg 151. Chapter 8. Study Question 1 and 2. Real GDP growth Rate = (31200-30000)/30000 * 100 = 4% GDP per Capita in year 1 = 30000/100 = 300 GDP Per Capital in year 2 = 31200/102 = 305.9 GDP per capita growth = (305.9-300)/300 = 1.96% Economic growth is a measure of the increase in the productive potential of a country. It is important because it reduces or lessens the problem of scarcity. Since it helps the economy to produce more, more goods are produced and everyone has more goods for consumption and as a result, living standard in the economy increases. This is why economists rate economic growth as a matter of great importance. We can use the 70 rule to determine the effect of the difference between 2.5 and 3 percent of economic growth over few decades. If an economy is growing at 2.5%, the economic growth or total output will double from the current level in 70/2.5= 28 years.

Education in Texas Essay Example | Topics and Well Written Essays - 750 words

Education in Texas - Essay Example Origins of Public Education in Texas The origins of the public education system in Texas grew out of the dissolution of an alliance between Mexico and Texas. Prior to 1835 the agreement between the two states stipulated that Mexico be responsible for education in that particular region of the United States. Because of the dissolution of the agreement and the enactment of the Texas Declaration of Independence of 1836 the responsibility of educating the public shifted from Mexico to the State of Texas. Major Milestones The education system in Texas has progressively evolved over the last 150 years. The development of the education system grew in response to the needs of the citizens and the demands of regional commerce. Some of the major historical milestones of the education system in Texas include: 1840 – First Anglo-American school opened; 17,712 acres of land in each county in the state designated for public schools (Texas Education Agency, 2011). 1845 – A specific pe rcentage of annual tax revenue set aside for free public education; creation of the Permanent School Fund (McClellan, 2011). 1876 – State Constitution of 1876 set aside 45 million acres of public lands for schools; funds held within the Permanent School Fund invested in bonds (Texas Education Agency, 2011). 1884 - School laws rewritten; re-creation of the duties and responsibilities of the State Superintendent of Education; ad valorem tax affirmed to create a consistent source of income for the public education system (Texas Education Agency, 2011). 1885 - Statewide school accreditation system developed and implemented (Texas Education Agency, 2011). 1949 - Senator A. M. Aikin and State Representative Claud Gilmer organize committees to reform education system (Gilmer-Aikin laws); teachers’ salaries and standardization of teaching credentials established (Erekson, 2010, p. 1033) 1957 – Assessment and evaluation of the effectiveness of the Gilmer-Aikin laws (Texa s Education Agency, 2011). 1984 - House Bill 72 increased teachers’ salaries and restructured school financing enabling a shift of resources from wealthier school districts to poorer performing districts (Texas Education Agency, 2011). 2001- No Child Left Behind (U.S. Department of Education, 2011). Reforms and Revisions The development of the education system, management agencies, state municipalities, along with individual school districts throughout the State has been an ongoing process. Pivotal events in the United States’ history such as the Civil War, World Wars I and II, and integration influenced the formation of the education system in Texas. From the inception and establishment of the first public school in 1840, leaders, elected administrators, and lawmakers sought ways in which to deliver the highest quality of education available for the residents of Texas (Texas Education Agency, 2011). Provisions for permanent funding for the education system did not occ ur until 1845 in which the Permanent School Fund was created. The fund created specific financing options for educating students in Texas; its purpose was to lighten the burden on citizens paying taxes and to produce an alternate way of funding public education. The predecessor of the Permanent Sch

Love is Love and Nothing Less Essay Example for Free

Love is Love and Nothing Less Essay In reflecting on my life as a child, adolescent, and adult, I have experienced love and lack of love on many occasions in the relationships I’ve experienced with others. To me, love is something that is present or is not present and cannot be split into various differing forms. I have never met the perfect, most ideal person who has loved me unconditionally, unendingly, and without interruption. The closest I’ve come to the ideal love has been through my religion, my spirituality, in my faithful relationship with God and Jesus Christ. However, even in this relationship, I have had my doubts, even if Jesus Christ, God, has never had them, so in this case as well, love has been interrupted. However, many of my relationships have incorporated loving actions, and it saddens me to recall the situations when love has been absent and hatred has crept into its place. Robert Sternberg has an interesting theory in regard to his attempt to separate out love and dissect it into varying forms, however, it is obvious that he often misses the mark in regard to what love means. The two categories which I consider to be rational evaluations of the presence or lack of presence of love are Sternberg’s two categories of nonlove and consummate love. To me, it’s always either one or the other, and one cannot assume to have a portion of love but not really, as if love has a grey area. In assuming that love has a grey or midrange area, one has to admit believing that badness mixes with good or that right and wrong are somehow united in a mesh of reality, however, in my opinion, good and good and bad is bad, wrong and right are separate, and ethics has to assume a position in regard to defining a loving way of being or loving action. Sternberg assumes that liking someone is only intimacy, devoid of passion and commitment, and in my opinion, this is illogical, as many loving relations with other people who I’ve considered friends or strangers, people who I’ve liked, have contained passion and commitment as well. Loving actions are filled with many aspects, and liking a person includes love, passion, commitment, respect, kindness, and many other values. To like someone most certainly includes having passion and commitment towards this other person. If we as a community and culture don’t have passion, commitment, and intimacy towards all members, then something is surely going wrong. Perhaps Sternberg is trying to imply that relationships with one’s spouse or family members are in some ways different from other relationships? If this is so, then he should focus on the unique attributes of playing the role of wife, son, father, or friend, and not focus on attempting to separate love into differing categories. The way one loves a person may vary, but love itself is constant. The idea that infatuation, fatuousness, or emptiness has anything to do with love is also unreasonable. How can love itself incorporate anything negative? Obsession, falsity, and voidance are certainly not aspects of love, passion, intimacy, or commitment. Has there ever been a time when being loving and kind to another person has incorporated elements of negativity? In and of itself, love is positive. It raises people up and makes them feel wonderful. In Sternberg’s attempt to triangulate love into three arenas, intimacy, passion, and commitment, he attempts to inject love with a poison of hatred or malevolence. If love is always good natured and good acting, then love cannot be split apart. People may, at times, at many times, cease to treat one another lovingly, cease to demonstrate the goods of intimacy, passion, and commitment, but that is simply the fault of the person and not an aspect of love itself. It is refreshing that Sternberg categorizes some of his love categories positively and not negatively, such as liking, romantic, companionate, and consummate, however this does not adequately explain or do justice to the fact that his other four supposed categories of love, nonlove, infatuated, empty, and fatuous are negatively termed. In my opinion, nonloving, infatuated, empty, and fatuous ways of behaving are part of hatred or evil and absent of love. If love is the right action in the right time and place with the right person, then love is fully good and absent of any mistakes. When Sternberg attempts to justify a divorce by claiming that the reason for the divorce is that one or both of the partners were loving one another, just loving one another differently, then he has certainly fallen prone to bad logic (Sternberg, 331). A divorce or a split is never caused by love, but rather by hateful or wrong actions by one person against another. It may be difficult to voice and communicate these wrong actions, however, a split, a lack of love, cannot be caused by love itself, but rather only by its absence. Although love shown towards one person or another may by expressed differently from one situation and person to the next, love itself is never aversive, yet rather uniting. The only culprit of divorce is the person behaving in nonloving ways. Sandelands very adequately states that the business of business is the human person. Everything that people do, everything that people were created by God to do, involves the spirit of the human person. Anyone believing that actions are just actions, that business is just business, devoid of the human person, has lost touch with the meaning of the high moral element of right action (93). In my own life, there have certainly been times when I acted in unloving ways towards other people, when I was empty of goodwill, false in my intentions. I remember lying to my mother, hurting my sisters, screaming at my father. My past boyfriends were often disgusted by my lack of fidelity. My daughter and husband are equally reviled by my bad manners when I overeat or eat sloppily. However, I also thankfully know that I have exuded love towards others. My father, mother, and sisters enjoyed it when I created a restaurant at home and cooked for everyone. My past boyfriends were often amused by my sense of humor in playfully lightening the moment. The caresses and kind words I offer to my husband and daughter are filled with benevolence, peace, and goodwill. It is in the interests of the whole of society to recognize that â€Å"caring as a virtue and an act of ethics is †¦ a natural †¦ point of view inseparably related to love as a universal †¦ value† (Arman Rehnfeldt, 4). When a person decides to love another person, any other person, then one consciously decides to do well towards another person and to not do badly toward another person. The sense that there is any type of human inaction proves false the fact that the universe is in constant motion. Every act or ceasing to act is directly related to cause and effect and can be categorized as fruitful or harmful. Although my mother may believe that being silent towards me is effectively loving and appropriate, I may believe that she does not love me. However, if I change my point of view and see that she is simply being silent and loving me by doing so, we come into agreement with one another and I cease to be negatively resistant to her goodwill. Also, if I loudly kiss my husband and he believes that I’m being sarcastic or hateful towards him, then I may very well be being sarcastic toward him in my actions. However, if I am aiming to love him in my kiss, then he himself is being paranoid for believing that I am not. We human beings are such sensitive creatures and it is often difficult to recognize and show love, however, the clear definition of love as a positive, ethical, valuable, and universal presence is vital in being able to correctly identify, demonstrate, and evoke loving actions. Erikson, a leader in the study of psychosocial human development, believes that people moving through the stage of young adulthood will pass through a phase of either attaining intimacy with a romantic partner or a friend or failing to achieve intimacy and becoming isolated (Goodman Mukulincer, 396). Although intimacy is important throughout the entire life of a person, perhaps it is good to note that young adulthood is primarily the time when people are selecting romantic partners and mates. Despite the fact that people from about puberty onwards toward death may seek romance with another person, many people on the search for romance are indeed young adults. However, it is very important, as in the case with Sternberg’s theory, not to box people in too much. Erickson’s ideas about intimacy and other issues related to life development are valid and worthy of consideration, but human beings crave and need intimacy from birth until death. Romantic love may be a special kind of love involving sexuality and more physical and deep interaction, reserved for one’s mate and life partner, however, love in general is necessary for every person, from conception until natural death. It would be good for people to open their hearts and minds up to the constancy of love and to make it a personal life goal or a life decision to work on demonstrating true self giving loving acts to everyone around them. Even though love may look different in varying situations between varying people, the underlying genuine goodwill is always there, love as a purposeful gift of positive and uplifting interaction. References Arman, M. Rehnsfeldt, A. (2006). The Presence of Love in Ethical Caring. Nursing Forum 41(1), 4-12. Goodman, G. Mikulincer, M. (2006). Dynamics of romantic love: attachment, caregiving, and sex. Guilford Press. Sandelands, L. (2009). The Business of Business is the Human Person: Lessons from the Catholic Social Tradition. Journal of Business Ethics 85, 93-101. Sternberg, R. Triangulating Love. The Altruism Reader, 331-333.

THE EVOLUTION OF CARIBBEAN SOCIAL POLICY Essay -- essays research pape

THE EVOLUTION OF CARIBBEAN SOCIAL POLICY: Reasons for the Changes and Shifts in the Social Policy Agenda From the 1940’s to the Present Period. Social Policy may be broadly defined as a system of social welfare that includes economic as well as non-economic objectives and involves some measure of progressive redistribution in command over resources1. Using Mishra’s typology of social welfare models (see Fig. 1 below), this paper describes the evolution of social policy in the English-speaking Caribbean. Drawing primarily from the experiences of Trinidad and Tobago and Jamaica, four chronological periods are used to highlight the factors contributing to the major developments in social policy: 1) the Immediate Post-War Period and the Moyne Commission (1940 to 1950); 2) Transition to Self-Government (1950 to 1961); 3) Ideology and the Immediate Post-Independence Period (1962 to 1973); 4) the Oil Crisis, World Recession and Structural Adjustment (1970 to 1980’s); 5) (Conclusion) The Present Period (1990 to present)2. A review of the literature revealed that a combination of social, economic, political/ideological and international factors contributed to policy development at each stage of this evolutionary process. This paper argues that as a result of these factors, Caribbean social policy gradually moved from a strong residual approach prior to the Moyne report, and tended to a more institutional approach during the transition period to full internal self-government, then to a more structural approach in the immediate post-independence period, and back to a residual approach when structural adjustment policies were instituted in the 1980’s. Of course, in reality the policies formulated in the various periods do not conform perfectly to Mishra’s types. However, this does not detract from the applicability of the model to the present analysis, as it is an inherent feature of all ideal types (as is implied by the descriptor â€Å"ideal†). Also, while the general factors contributing to the evolution of Caribbean social policy has been highlighted, the specific ways in whi ch these factors manifested in each country are extensively discussed. Fig. 1 Mishra’s Welfare Models1 Main Features Type of Welfare Residual Institutional Structural State responsibility in meeting needs (ideology of state intervention) Minimal Optimal... ... Henry, Ralph and Moesire, Alicia. â€Å"Poverty Alleviation and Reduction Programmes: the Commonwealth Caribbean Experience† in Poverty, Empowerment and Social Development in the Caibbean. Ed, Norman Girvan. Mona: Canoe Press UWI, 1997, 101 – 136. Mac Pherson, Stewart. Social Policy in the Third World: The Social Dilemmas of Underdevelopment. UK: Wheatsheaf Books Ltd. 1982. Neil, Joan. Targeting and Poverty: New Trends in Social Policy – Social Projects for Alleviation in the Republic of Trinidad and Tobago. UNECLAC, 1992. Robothom, Don. Social and Economic Policy: Starting Gates and End-States, UWI, 1995. Sinha, D.P. â€Å"Health Care of The Population† in Children of the Caribbean. CFNI/PAHO, 198 8. 123-144. Stone, Carl. â€Å"Power Policy and Politics in Independent Jamaica† in Jamaican in Independence: Essays on the Early Years. Ed, Rex Nettleford. Kingston: Heinemann Caribbean, 1989, 19-53. Thomas, Clive, Y. â€Å"The interrelationship between economic and social development† in Poverty, Empowerment and Social Development in the Caribbean. Ed, Norman Girvan. Mona: Canoe Press UWI, 1997, 20-49. Titmuss, R. Social Policy: An Introduction.

Limit

Q1. What is the difference between a left neighborhood and a right neighborhood of a number? How does this concept become relevant in determining a limit of a function? Answer: Left neighborhood of a number ‘a’ represents numbers lesser than the number ‘a’ and is denoted by ‘a-’ or ‘a-d’, where d is infinitesimally small. Similarly, right neighborhood of a number ‘a’ represents numbers greater than the number ‘a’ and is denoted by ‘a+’ or or ‘a+d’, where d is infinitesimally small. This concept is very important in determining limit of a function. A function f(x) of ‘x’ will have a limit at x = a; if and only if f(a-d) = f(a+d) = f(a); where d is infinitesimally small. Q2. A limit of a function at a point of discontinuity does not exist. Why? Give an example. Answer: For existence of limit of function f(x) of ‘x’; at x = a; the necessary and sufficient condition is f(a-d) = f(a+d) = f(a); where d is infinitesimally small. At a point of discontinuity, f(a-d) ≠  f(a+d). Therefore, limit of a function does not exist at a point of discontinuity. The following example will make it clear. Let us take example of integer function. This function is defined in the following manner: f(x) = a;  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   where ‘a’ is an integer less than or equal to x. Let us check if limit exists for this function at x = ‘a’, where ‘a’ is an integer. Now left hand side limit = f(a-d) = a-1 And right hand side limit = f(a+d) = a Thus, f(a-d) ≠  f(a+d); and hence limit does not exists for this function. If this function is plotted, there is discontinuity at all integer points. Thus it can be seen that limit of a function does not exist at a point of discontinuity. 3. What is the difference between a derivative of a function and its slope? Give a detailed explanation. Answer: Derivative of a function is another function, which remains same throughout the domain of the function at all the points. Slope of a function on the other hand is the value of the derivative. This value may change from point to point depending on the nature of the function. Let us take an example. Derivative of Sin(x) is Cos(x) for all values of ‘x’. If one looks at the slope of Sin(x), its value keeps changing in [-1, +1] range from point to point. Slope of Sin(x) is -1 for x = odd integral multiples of p; +1 for x = even multiples of p and 0 for x = odd multiples of p/2. Thus, it can be seen that while derivative of a function remains the same while its slope could be changing from point to point.