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Left-hand limit at a point Let s expand the domain of f to the entire set of reals except 0, for which f is not defined because 0 1 is meaningless Suppose that we start out with negative real values of x and approach 0 from the left As we do this, f decreases endlessly Another way of saying this is that f increases negatively without limit, or that it blows up negatively Therefore,

x 0

Since we are unlikely to nd the perfect blend of skills and personality, we will need to evaluate each person in both areas, and then decide who is best for the job. In some projects and roles, such as those that require speci c engineering, programming, or other professional skills, the technical quali cations are most important. In other projects or roles, the teamwork skills are most important, and a willing person can pick up the knowledge to do the job.

Lim f (x )

111 order for T/T,

is not defined We read the above symbolic expression as, The limit of f (x) as x approaches 0 from the negative direction We can also say, The limit of f (x) as x approaches 0 from the left This sort of limit is called a left-hand limit

Technical skills can be derived from the WBS. If we or experts in the appropriate elds look at the WBS, we will be able to say what professional skills, and what level of skill, are required for each job. If you are managing a technical project in an area outside your expertise, be careful. It can be more complicated than you might think. For example, setting up a web page can require any of these skills: computer graphics design; ability to use a web tool such as Microsoft FrontPage or Macromedia DreamWeaver ; ability to write HTML code; ability to write scripts in a programming language such as JavaScript or PHP; and the ability to put all of this together, send it to a web site, and make it work. One person is unlikely to have all of these skills. Exactly which ones does your project need To nd out, get expert help de ning the tasks in the WBS. Then write a job description, and look for people with many of the skills you need. When you do, you will also need to be concerned with the level of skill. Is the person trained in school Certi ed How many months or years of experience does the applicant have using skills relevant to this job Can you take a look at samples of work done In looking at a person s skill level, we will need to assess: appropriateness of skill to the project; ability to deliver quality work; and speed or productivity in a limited time. Which of these is most important for your current project

An example Let s consider a function g that takes the reciprocal of twice the independent variable If the independent variable is x, then we have

g (x ) = (2x ) 1 Imagine that we allow x to be any positive real number As x gets arbitrarily large positively, g (x) gets arbitrarily small positively, approaching 0 but never quite getting there We can say, The limit of g (x ), as x approaches infinity, is 0, and write Lim g (x) = 0

x

A project is a team e ort on a tight deadline. This de nes the key skills required for people on projects and teams. Key skills for people on projects include: Ability to get work done and delivered on time. A start-driven focus. We want people who will start a job as soon as they can, not ones who will wait until a deadline is pressing. Self-responsibility.

This scenario is similar to what happens with the reciprocal function, except that this function g approaches 0 at a different rate than the reciprocal function as the independent variable becomes arbitrarily large Now let s see what happens when x gets smaller but stays positive, so that g (x) gets larger If we make x close enough to 0, we can make g (x) as large as we want This function, like the reciprocal function, blows up as x approaches 0 from the positive direction, but at a different rate Therefore

i&P-

Lim g (x )

x