lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 .
(a) On what open intervals contained in 0
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48.A new viral illness was recently identified in the community. The virus caused people to develop “Itchy hand
disease” (IHD) –
...
Itchy hand
disease” (IHD) – a disorder characterised by muscle aches and pains, fever and an itchy rash on the hands and
feet. Itchy hand disease is thought to have a higher incidence in older persons and smokers. Dr Boisty was
interested in determining whether healthcare workers were more at risk of developing IHD than were workers
in other sectors and decided to investigate this issue.
Five hundred health care workers were recruited into the study. They were compared to 700 office workers.
Both groups were followed for six months. During follow-up, any presentation to a doctor was notified to the
study team, who contacted the doctor to find out what the diagnosis was. The outcome of interest was IHD. Of
the 500 health care workers, 43 developed IHD during the study. Of the 700 office workers, 23 developed IHD
during the study.
Dr Boisty knew that many members of the community liked to take a supplement called Herbal Extract X (‘HEX’)
to try to “boost their immune system”. Herbal Extract X was also suspected of causing IHD. So, Dr Boisty
collected information on the use of HEX by the study participants.
Of the health care workers, 400 used HEX; 39 of these developed IHD. Of the office workers, 300 used HEX; 15
of these developed IHD.
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