During a controlled experiment

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

During a controlled experiment, the height

H

(in metres) of water in a tank is monitored over six hours. The height changes according to

H(t)=\begin{cases} 5-0.5t, & 0\le t\le 2,\\ 7, & t=2,\\ 7-0.25\,(t-2), & 2<t\le 6, \end{cases}

where

t

is the time in hours after the start of the experiment. (a) Part 1: (i) Sketch the graph of

H

for

0\le t\le 6

on your answer sheet, clearly indicating any open or closed points. (b) Part 2: (ii) Identify all times in

[0,6]

at which

H

is not continuous and classify each discontinuity as removable, jump or infinite. Give reasons based on one-sided limits and the value of

H

at the point, when defined. (c) Part 3: (iii) Is

H

continuous on the closed interval

[0,6]

according to the textbook definition? Justify your answer briefly.