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Recitation 16   \hfill \course\\
15 October 1998  \hfill \semester \\

\medskip

{\bf Reminders}: 
1. A notebook is on reserve in the math library for this course. This
notebook  contains tests from last year and  solutions to tests,
homework, quizzes and 
projects. The math library is located in the basement of the Patterson
Office  Tower. 

2. The second exam will be Tuesday night, 20 October from 7:30 to
9:30 in CB114.

3. The last homework assignment for Chapter 2 is \S2.9 \#12, \S2.10
\#16. This assignment is due on Monday, 19 October at the beginning of
class.

4. There is a quiz on Friday, 16 October.

5. The last day to withdraw is 23 October. After the second test is
returned, you will have the opportunity to compute your midterm
grade and you may wish to use this information to help decide if you
will continue in this course.


\medskip
 
Below is a selection of problems related to sections 2.9 and 2.10.
These problems will not be collected or graded. However, you should
understand how to work each of these problems.  You should begin
working on these problems in groups in recitation. You will probably
want to finish these problems outside of class. 
 If you have questions,
please ask your TA or instructor. If you find a problem difficult,
consider working similar problems from the text for additional practice.

\begin{enumerate}


\item (Review) Rationalize the denominator
$$
\frac 1 { \sqrt 2 + \sqrt 3}.
$$

\item (Review) Find the limits using the limit laws:
$$
\lim _{x\rightarrow \infty} {x^2 + 1} { x^2 -1}, \qquad 
\lim _{ x\rightarrow 1 } {x^2-x} {x^2-1}.
$$

\item (Review) Let $$
f(x) = \left\{ \begin{array}{ll} 
x \qquad & x\leq -1 \\
2x \qquad & -1 < x \leq 2 \\
x+2 \qquad & 2\leq x 
	       \end{array}
\right.
$$
For which $x$ is this function continuous? For which $x$ is this
function differentiable? Justify your answers.

\item (Review) Find the following limits.
$$
 \lim_{x\rightarrow 1 } \frac { x^2 +1 }{x^2-1} \qquad 
\lim _{x\rightarrow \infty} e^x\qquad \lim_{x\rightarrow \infty } \ln
x$$

\item Section 2.9 \#1, 3, 5, 11.
\item Section 2.10 \# 1, 3, 9, 11, 15, 21, 23, 26.


\end{enumerate}

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