Homework 2

1.  Explain in your own words what is meant by the equation  

Is it possible for this statement to be true and yet

2. Explain what it means to say that

$\underset{x\to 1^{–}}{\lim } f\left(x\right) = 3 and \underset{x\to 1^{+}}{\lim } f\left(x\right)=7$

In this situation is it possible that

  Explain.

3.  Explain the meaning of each of the following.

$\left(a\right) \underset{x\to –3}{\lim }f\left(x\right) = \infty \left(b\right) \underset{x\to 4^{+}}{\lim }f\left(x\right) = –\infty$

4.  Use the given graph of f to state the value of each quantity, if it exists.  If it does not exist, explain why.

$$\begin{gathered} \left(a\right) \underset{x\to 2^{–}}{\lim }f\left(x\right) \left(b\right) \underset{x\to 2^{+}}{\lim }f\left(x\right) \left(c\right) \underset{x\to 2}{\lim }f\left(x\right) \\ \left(d\right) f\left(2\right) \left(e\right) \underset{x\to 4}{\lim }f\left(x\right) \left(f\right) f\left(4\right) \end{gathered}$$

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

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

$$\begin{gathered} \left(a\right)\underset{x\to –3^{–}}{\lim }h\left(x\right) \left(b\right) \underset{x\to –3^{+}}{\lim }h\left(x\right) \left(c\right) \underset{x\to –3}{\lim }h\left(x\right) \\ \left(d\right) h\left(–3\right) \left(e\right) \underset{x\to 0^{–}}{\lim }h\left(x\right) \left(f\right) \underset{x\to 0^{+}}{\lim }h\left(x\right) \\ \left(g\right) \underset{x\to 0}{\lim }h\left(x\right) \left(h\right) h\left(o\right) \left(i\right) \underset{x\to 2}{\lim }h\left(x\right) \end{gathered}$$

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

$$\begin{gathered} \left(a\right) \underset{t\to 0^{–}}{\lim }g\left(t\right) \left(b\right) \underset{t\to 0^{+}}{\lim }g\left(t\right) \left(c\right) \underset{t\to 0}{\lim }g\left(t\right) \\ \left(d\right) \underset{t\to 2^{–}}{\lim }g\left(t\right) \left(e\right) \underset{t\to 2^{+}}{\lim }g\left(t\right) \left(f\right) \underset{t\to 2}{\lim }g\left(t\right) \\ \left(g\right) g\left(2\right) \left(h\right) \underset{t\to 4}{\lim }g\left(t\right) \end{gathered}$$

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

$$\begin{gathered} \left(a\right) \underset{x\to –3}{\lim }A\left(x\right) \left(b\right) \underset{x\to 2^{–}}{\lim }A\left(x\right) \\ \left(c\right) \underset{x\to 2^{+}}{\lim }A\left(x\right) \left(d\right) \underset{x\to –1}{\lim }A\left(x\right) \\ \left(e\right) The equations of the vertical asymptotes \end{gathered}$$

9.  For the function f whose graph is shown, state the following:

$$\begin{gathered} \left(a\right) \underset{x\to –7}{\lim }f\left(x\right) \left(b\right) \underset{x\to –3}{\lim }f\left(x\right) \left(c\right) \underset{x\to 0}{\lim }f\left(x\right) \\ \left(d\right) \underset{x\to 6–}{\lim }f\left(x\right) \left(e\right) \underset{x\to 6+}{\lim }f\left(x\right) \end{gathered}$$

(f) The equations of the vertical asymptotes

10.  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

$\underset{t\to {12}^{–}}{\lim }f\left(t\right) and \underset{t\to {12}^{+}}{\lim }f\left(t\right)$

and explain the signficance of these one-sided limits.