\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Let $a$ be a positive constant and
consider the functions
$$
f(x)=\arcsin\left({x\over a}\right)\hbox{ and } g(x)=a \arctan \left({x\over
a}\right).
$$
Find the derivatives of $f$ and $g$ and express them in as simple a
form as possible. There is a certain value of $a$ for which the lines
tangent to the graphs of these two functions at $x=1$ are parallel
lines. Find that value of $a$ to $3$-place accuracy. (Find an exact
equation satisfied by $a$, and then get an accurate enough solution
from your calculator.) 


%1.168261

\vfil\eject\end