A storage tank is being filled with a liquid that is kept at a temperature (in…
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A storage tank is being filled with a liquid that is kept at a temperature T (in degrees Celsius) that varies over time. The temperature is recorded continuously during the interval 0≤t≤10 minutes. A graph of y=T(t) on this interval is described below.
• For 0≤t≤4, the graph is a straight line segment that rises from (0,55) to (4,62).
• Between t=4 and t=6, rapid fluctuations occur: the graph oscillates smoothly between 61 and 63 degrees completing three full oscillations, ending at an open circle located at (6,62).
• For t>6, the temperature stabilizes; the curve is a nearly horizontal segment that begins at the open point (6,62) and approaches the closed point (10,61.8) without additional oscillations.
Answer the following questions about the temperature at t=6 minutes.
(a) Estimate t→6−limT(t) and t→6+limT(t). Support each estimate with specific features of the described graph.
(b) Determine whether t→6limT(t) exists. Justify your conclusion in the context of the left-hand and right-hand behavior found in part (a).
(c) Interpret the meaning of your result from part (b) in terms of the physical situation of the liquid’s temperature at exactly t=6 minutes.