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   \begin{center}
     {\bf MTH112 -- TEST 4}
   \end{center}

\begin{flushright}
   Name: \rule[0in]{1.5in}{.01in}
\end{flushright} \vs

\noin HONOR CODE: On my honor, I have neither given nor received 
any aid on this examination. \\
Signature: \rule[0in]{1.5in}{.01in}

\noin Note: Show all work on exam in order to receive full credit. 

\begin{enumerate}
\item  Determine whether the sequence converges or diverges. If
it converges, find the limit.
	\begin{enumerate}
	\item $\ds \frac{4n-3}{3n+4} $
	\vspace{4cm}\item $\ds  \ln(n+1)-\ln n$
	\vspace{4cm}\item $\ds \frac{(-3)^n}{n!}$
	\end{enumerate}

\newpage
\item Determine whether the series is convergent or divergent. If
it is convergent, find its sum.
	\begin{enumerate}
	\item $\ds \sum_{n=1}^{\infty}\frac{1}{e^{2n}}$
	\vspace{4cm}\item $\ds \sum_{n=1}^{\infty} \frac{n^2}{3(n+1)(n+2)}$
	\vspace{4cm}\item $\ds \sum_{n=2}^{\infty} \ln\frac{n^2-1}{n^2}$
	\end{enumerate}

\newpage
\item Determine whether each integral is convergent or divergent. 
Evaluate those that are convergent.
	\begin{enumerate}
	\item $\ds \int_0^\infty \frac{x}{(x+2)(x+3)}\, dx$
	\vspace{4cm}\item $\ds \int_{-\infty}^\infty e^{-|x|}\,dx$
	\vspace{4cm}\item $\ds \int_0^2\frac{1}{4x-5}\,dx$
        \end{enumerate}

\newpage
\item Use comparison tests to determine whether the series is convergent or divergent.
{\em Do not} evaluate the convergent sums.
	\begin{enumerate}
    	\item $\ds \sum_{n=1}^{\infty}\frac{\sin^2 n}{n \sqrt{n}}$
	\vspace{4cm}\item $\ds \sum_{n=1}^{\infty}\frac{n}{(n+1) 2^n}$
	\vspace{4cm}\item $\ds \sum_{n=1}^{\infty}\frac{3n^3 -2n^2}{n^4 +n^2+1}$
 	\end{enumerate}

\end{enumerate}
\end{document}




