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\textbf{Math 126: Calculus II}
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\textbf{Quiz 1}\quad \textsl{Aug. 31, 1999}
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1.  In the plot below, you will find the graph of a function 
\begin{math}
  y=f(x)
\end{math}
together with the graph of 
\begin{math}
  y=x.
\end{math}


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a. On this plot, graph the inverse of 
\begin{math}
  f.
\end{math}

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b.  Estimate 
\begin{math}
  {\frac {df}{dx}(0.25)}
\end{math}
and 
\begin{math}
  {\frac {d(f^{-1})}{dx}(f(0.25))}.
\end{math}

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\begin{math}
{  \frac {df}{dx}(0.25)=}
\end{math}
\underline{\hspace{0.5in}}
\hspace{1in}
\begin{math}
  {\frac {d(f^{-1})}{dx}(f(0.25))=}
\end{math}
\underline{\hspace{0.5in}}



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\ 

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2. Evaluate 
\begin{math}
 { \int _1^{\mathbf e} \frac 1{x\sqrt{\ln x}}\,dx,}
\end{math}
carefully {\bf showing your work} and {\bf all} important steps.
 
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