A temperature probe records readings (in degrees Celsius) every minute during a…
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A temperature probe records readings (in degrees Celsius) every minute during a laboratory experiment. The display resets the timer so that t=5 corresponds to an important chemical event. A segment of the numerical output is reproduced below.
t (minutes)
4.7
4.8
4.9
4.95
5.05
5.1
5.2
Temp(t)
68.1
68.4
68.9
69.0
57.5
69.2
69.4
(a) Identify any observation(s) in the table that could be regarded as an outlier relative to the surrounding data. Justify your choice quantitatively.
(b) Using only the non–outlier values, estimate t→5limTemp(t). State your estimate and explain your reasoning.
(c) Explain, in complete sentences, why the presence of the outlier causes a naive observer to draw an incorrect conclusion about the existence of the limit as t→5. Include a discussion of how a single erroneous data point can mimic a jump discontinuity.