Answer
$(a)$ $\lim_{t\to4}f(t)=0$
$(b)$ $\lim_{t\to-1}f(t)=-5$
Work Step by Step
$f(t)=t|t-4|$
The graph of the function is shown below:
$(a)$ $\lim_{t\to4}f(t)$
From the graph, it can be seen that when $x$ approaches $4$ from the left and from the right, $f(t)$ approaches $0$
$\lim_{t\to4}f(t)=0$
$(b)$ $\lim_{t\to-1}f(t)$
From the graph, it can be seen that when $x$ approaches $-1$ from the left and from the right, $f(t)$ approaches $-5$
$\lim_{t\to-1}f(t)=-5$
