David M.

The table shows the position of a motorcyclist after accelerating from rest.

(a) Find the average velocity for each time period:
(i) $ [2, 4] $ (ii) $ [3, 4] $ (iii) $ [4, 5] $ (iv) $ [4, 6] $
(b) Use the graph of $ s $ as a function of $ t $ to estimate the instantaneous velocity when $ t = 3 $.

For the function $ f $ whose graph is given, state the value of each quantity, if it exists. If it does not, explain why.

(a) $ \displaystyle \lim_{x\to 1}f(x) $
(b) $ \displaystyle \lim_{x\to 3^-}f(x) $
(c) $ \displaystyle \lim_{x\to 3^+}f(x) $
(d) $ \displaystyle \lim_{x\to 3}f(x) $
(e) $ f(3) $

For the function $ h $ whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{x\to -3^-}h(x) $
(b) $ \displaystyle \lim_{x\to -3^+}h(x) $
(c) $ \displaystyle \lim_{x\to -3}h(x) $
(d) $ h(-3) $
(e) $ \displaystyle \lim_{x\to 0^-}h(x) $
(f) $ \displaystyle \lim_{x\to 0^+}h(x) $
(g) $ \displaystyle \lim_{x\to 0}h(x) $
(h) $ h(0) $
(i) $ \displaystyle \lim_{x\to 2}h(x) $
(j) $ h(2) $
(k) $ \displaystyle \lim_{x\to 5^+}h(x) $
(l) $ \displaystyle \lim_{x\to 5^-}h(x) $

For the function $ g $ whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{t\to 0^-}g(t) $
(b) $ \displaystyle \lim_{t\to 0^+}g(t) $
(c) $ \displaystyle \lim_{t\to 0}g(t) $
(d) $ \displaystyle \lim_{t\to 2^-}g(t) $
(e) $ \displaystyle \lim_{t\to 2^+}g(t) $
(f) $ \displaystyle \lim_{t\to 2}g(t) $
(g) $ g(2) $
(h) $ \displaystyle \lim_{t\to 4}g(t) $

For the function $ A $ whose graph is shown, state the following.

(a) $ \displaystyle \lim_{x\to -3}A(x) $
(b) $ \displaystyle \lim_{x\to 2^-}A(x) $
(c) $ \displaystyle \lim_{x\to 2^+}A(x) $
(d) $ \displaystyle \lim_{x\to -1}A(x) $
(e) The equations of the vertical asymptotes

A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount $ f(t) $ of the drug in the bloodstream after $ t $ hours. Find
$ \displaystyle \lim_{t\to 12^-}f(t) $ and $ \displaystyle \lim_{t\to 12^+}f(t) $
and explain the significance of these one-sided limits.