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These extracts are from M208 © 2006 The Open University.

 

All material contained within this unit originated at The Open University.


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2 Real functions

In Section 1 we formally define real functions and describe how they may arise when we try to solve equations. We remind you of some basic real functions and their graphs, and describe how some of the properties of these functions are featured in their graphs.

Click 'View document' below to open Section 1 (12 pages, 1.8MB).

Introduction

Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful skill, even though computer packages can now perform the task. Computers can plot many more points than can be plotted by hand, but simply ‘joining up the dots’ can sometimes give a misleading picture, so an understanding of how such graphs may be obtained remains important. The object of t
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Acknowledgements

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1. Join the 200,000 students currently studyi
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3.2.1 Try some yourself

1 Use the method outlined in Example 9 to estimate each of the following, and then use yo
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3.1.1 Try some yourself

1 Express each of the following numbers in scientific notation.

  • (a) Light travels 9460 700 000 000 km in a year.

  • (b) The average distance from the centre of the Earth to the centre o
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3.1 Expressing numbers in scientific notation

Earlier you looked at place values for numbers, and why they were called powers of ten.

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1.1.1 Try some yourself

1 On the plan of the bathroom in Example 1, what is the width of the window and
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1.6.3 Mailing lists and newsgroups

Mailing or discussion lists are email-based discussion groups. When you send an email to a mailing list address, it is sent automatically to all the other members of the list.

The majority of academic-related mailing lists in the UK are maintained by Jiscmail. You will find details of joining these mailing lists on the Jiscmail website. Mailing lists are useful for getting in touch with like-minded colleagues. They are also handy for keeping up to date with current thinking and research
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6.4 International retributive justice

A further difference between communitarians and cosmopolitans arises over the question of retributive justice. Communitarians think that it is the responsibility of each state to uphold justice. Collectively, states can pursue international justice through the auspices of the UN, and are answerable to each other, to public opinion and to NGOs. However, there is no basis for claims to universal jurisdiction, and to deal with matters not found in specific states (such as piracy), or that cross
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5.5 Feminist critiques of international rights

The second source of criticisms that we would like to explore comes from feminist critiques. Some feminists argue that the universal notion of rights makes invisible the special problems faced by women as a group, and that, thereby, specific articles of the various human rights declarations and conventions reinforce traditional gender roles in the family and the workplace. This criticism comes in at least two forms.

The first is that rights for women (as for other disadvantaged groups)
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2.1 Background to the idea of international rights

The UN Charter and the Declaration form part of a post-Second World War international settlement which established, on the one side, the formal legitimating ideology of the international system, national self-determination and sovereign equality and, on the other, the ideology of universal human rights. The appeal of this set of claims was the hope that different peoples could live together in peace and security. It was an attempt to accommodate difference (through the idea of national self-d
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5 Conclusion

The issue of climate change draws attention to the power of human activity to transform the planet in its entirety, and it is brought into sharp focus by the predicament of low-lying islands like Tuvalu. As we have seen in this unit, the issue of rising sea level and other potential impacts of changing global climate also point to the transformations in the physical world that occur even without human influence. Oceanic islands provide a particularly cogent reminder that the living things wit
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Introduction

The unit uses the example of climate change to highlight the dynamic and volatile character of the planet, and how globalisation links together, in often unequal ways, people and places across the world. The unit focuses on the potentially momentous impact of global environmental change on Pacific Islands like Tuvalu. It introduces students to geographical ways of thinking about the world.

This unit is an adapted extract from the Open University course
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Acknowledgements

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Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit.

Every effort has
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4.2 Environmental and labour standards

Question

Look back at Section 1. Why do trade unions in rich countries take up the cause of poor environmental and working conditions in developing countries as they did at Seattle? And why are developing country governments unwilling
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2.3.2 The project (single) team

The project, or single, team consists of a group of people who come together as a distinct organisational unit in order to work on a project or projects. The team is often led by a project manager, though self-managing and self-organising arrangements are also found. Quite often, a team that has been successful on one project will stay together to work on subsequent projects. This is particularly common where an organisation engages repeatedly in projects of a broadly similar nature – for e
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6.3.1 Prototyping

The first prototypes may be made of any convenient material, such as clay, plaster-of-Paris or wood. Plastic models can also be made by fabrication or vacuum forming of thin sheet. Their primary function is to ensure that the product has ‘customer appeal’ when considered in aesthetic or ergonomic terms. This is particularly important for products which are to be consumer durables. It may be the first time in the design process that the concept sketches and initial engineering drawings are
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3.3.3 Higher aromatics

Benzene rings can be fused in various ways to create component parts for some of the complex aromatic repeat units shown in Table 5. One of the most important is bisphenol A, made by fusing two phenol rings with acetone:

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4.5 Torture

The question of torture is also raised in the play. Herrenvolk claims that he does not do the torture; it is some Uzbekistan outfit that does it. He actually gives them a justification by saying, in a rather glib way, that it is a lot easier to open a human being than an encrypted laptop. Of course, the question is, is it ever ‘right’ to exploit this as a means of finding things out? I suspect most of us would say ‘no’.


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