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\begin{flushleft} 
Recitations 21--24   \hfill \course\\
3, 5, 10, 12 November 1998  \hfill \semester \\

\medskip

Below is a selection of problems related to sections 3.5 to 4.1.
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.

\bf Announcement: \rm Brown will be out of town on 9--13
November. Jeff Sykes
will lecture for this week. All classes will meet as scheduled. 


\begin{enumerate}

\item Here are the last two written homework assignments for Chapter 3
and section 4.1.

\begin{itemize}
\item Due Wed, 11 November 1998. \S3.6 \# 22, 46 \S3.7 \# 22, 30.

\item Due Monday, 16 November 1998. \S 3.8 \#16, \S4.1\#12, 24.

\end{itemize}


\item \S3.5 \#1, 3, 7--30 (work as many as you need to feel confident
				with rules of differentiation), 31,
43, 45, 47, 50, 51, 61, 63, 67a)  (Don't use induction on 67a), I
think.)

\item \S3.6 \#3, 11, 13, 15, 21, 33, 37, 45.=20

\item Let $y=f(x)$ be the inverse function for $ x= \sin y$ where the
domain of $\sin y$ has been restricted to the interval $(\pi/2, 3\pi
/2)$.  Note that $f$ is not the standard inverse function,
$\sin^{-1}$. 

\begin{enumerate} \item Sketch the graph of $\sin x$, for $x$ in $(\pi
/2, 3\pi/2)$ and the graph of the inverse function. Based on your
graph, is $ f'$ positive or negative? (Hint: Remember that if we know
the graph of a function, the graph of the inverse function is found by
reflecting in the line $y= x$.) 

\item Use that $ x= \sin (f(x))$ and implicit differentiation to find
the derivative $f'(x)$. 

\item Your answer to the previous part may contain a trigonometric 
function and $f(x)$.  Use the Pythagorean identity, $\cos^2 u + \sin^2 u =
 1$, to  express $f' $ in terms of $x$.    Hint:  Be careful when you 
take the square root.  

\item Is your expression for $f'$ different from the expression for
the derivative of $\sin ^{-1}$ found on page 244?  Explain why.
\end{enumerate}

\item \S3.7 \#3, 5, 7, 9 (simplify first), 15, 23, 25, 29.

\item \S3.8 \#1, 3, 7, 9, 11, 15.

\item \S4.1 \#1, 3, 5, 7, 9, 11, 13, 23, 25.

\end{enumerate}
\end{flushleft}

\noindent{\small  \today }
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