Chapter 1.2, Problem 85E

A lab technician controls the temperature T inside a kiln. From an initial temperature of 0 degrees Celsius $\left(°\text{C}\right)$, he allows the temperature to increase by $2°\text{C}$ per minute for the next 60 minutes. After the 60^th minute, he allows the temperature to cool by $3°\text{C}$

per minute. If t is the number of minutes, the temperature T is given by

$T\left(t\right)=\{\begin{array}{l}2t,\text{for}t\le 60,\\ 300-3t,\text{for}t>60.\end{array}$

Find $\underset{t\to {60}^{-}}{\lim }T\left(t\right),\underset{t\to {60}^{+}}{\lim }T\left(t\right),\text{and}\underset{t\to 60}{\lim }T\left(t\right)$.