The temperature (in °C) of a chemical solution is recorded every second
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
The temperature T (in °C) of a chemical solution is recorded every second. A portion of the data collected near t=12 s is shown below.
t (s) 11.900 11.990 11.999 12.001 12.010 12.100
T (°C) 23.92 23.99 23.999 24.001 24.010 24.08
The measuring device malfunctioned exactly at t=12 s, so T(12) was not recorded.
(a) Estimate t→12limT(t) to four decimal places.
(b) Explain why your estimate in part (a) is reasonable by describing the trend of T(t) as t approaches 12 from both sides.
(c) Suppose the sensor later reports that T(12)=23.10 °C. Discuss whether this reported value is consistent with the limit you found, and determine if T is continuous at t=12 under this reported value.
(d) Determine a value that could be assigned to T(12) to make T continuous at t=12. Justify your choice.