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is undefined at . However, if , you can cancel the factors, and the equation becomes
So is a quadratic function with a removable discontinuity at (Figure ). The -value at this missing point is the limit of as approaches 2 . Figare
a. Show that has the indeterminate form . What feature does the graph of have at ? Do an appropriate calculation to show that 5 is the limit of as approaches 2 .
b. Find the interval of -values close to 2 , but not including 2 , for which is within unit of 5 . Keep at least six decimal places for the -values at the ends of the interval. Based on your answer, what is the largest value of for which is within unit of 5 when is kept within unit of 2 ?
c. Draw a sketch to show how the numbers , , and in the definition of limit are related to the graph of in this problem.
In 2014, in an experiment conducted in cooperation with the National Institute of Nuclear Physics CUORE, Gran Sasso at the highest peak in the Apennines, about 120 kilometers away from Rome. Scientists from the Italian Institute set the world record for the lowest temperature observed In the universe. They cooled a cubic meter of copper container to -273,144 degrees Celsius.
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