Questions: where t is time in years since 2010. (You can click on the graph to enlarge it.) Find the following limits. Use DNE for "does not exist" when applicable. a. lim t→5− m(t)= □ b. lim t→5+ m(t)= □ c. lim t→5 m(t)= □

Solution Steps

The graph shows that as \(t\) approaches 5 from the left, the value of \(m(t)\) approaches 0.75. Therefore, $\lim_{t \rightarrow 5^{-}} m(t) = 0.75$.

The graph shows that as \(t\) approaches 5 from the right, the value of \(m(t)\) approaches 1.05. Therefore, $\lim_{t \rightarrow 5^{+}} m(t) = 1.05$.

Since the left-hand limit and right-hand limit are not equal, $\lim_{t \rightarrow 5^{-}} m(t) \ne \lim_{t \rightarrow 5^{+}} m(t)$, the limit $\lim_{t \rightarrow 5} m(t)$ does not exist.

Final Answer