

\magnification1200\footline{}
\centerline{\bf Math.~126 Quiz \#7}
\centerline{March 16, 1999}
\vskip10pt
\def\frac#1#2{{{\textstyle#1}\over{\textstyle#2}}}
\def\Int{\displaystyle\int}

\noindent{\bf 1.} Which of these integrals is {\sl improper\/}?
No reasons need be given - just a list of the letters (a-d)
for the improper ones.
$$\matrix{%
{\rm a.}&\Int^\infty_0 e^{-x}dx&\qquad&
{\rm b.}&\Int_{-1}^1\frac{dx}{x}\cr
{\rm c.}&\Int_{-1}^1{\sqrt{1-x^2}}\>dx&&
{\rm d.}&\Int_{-1}^1\frac{dx}{\sqrt{1-x^2}}\cr
}$$


\vskip 1in
\noindent{\bf 2.}
For which values of $r$ does
$\Int_{0}^{3}x^r\>dx$ converge?
Be sure to consider both positive and negative values.
For this problem, some reasoning should be given for
your conclusions.

\end


Sent Thu Mar 11 19:46:30 EST 1999
