Question 1
Find the intervals on which the function is continuous.
Is the function given by f(x) =
continuous continuous on ℛ?
◦ Yes, f(x) is continuous at each real number
◦ No, since f(x) is not continuous over the interval
Question 2
A biologist controls the humidity H (as a percentage) inside a terrarium. From an initial humidity level of 0%, she allows the humidity in the terrarium to increase by 1% per hour for the next 6 hours. After the 6th hour, she allows the terrarium to dry out (lose humidity) at the rate of 5% per hour. The humidity function H is defined by
H(t) =
Find k such that H is continuous at t = 24. Then explain why H must be continuous at t = 6 hours.
◦ k = 36; H must be continuous at t = 6 hours because the humidity level changes continuously.
◦ k = 174; H must be continuous at t = 6 hours because time changes continuously.
◦ k = 24; H must be continuous at t = 6 hours because the humidity level changes continuously.
◦ k = 186; H must be continuous at t = 6 hours because time changes continuously.
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