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\problemgrouptitle{Improper Integrals}

\begin{problemblock}[2]{Determine whether the given integral is convergent or divergent.}
\addtoanswerkey{\begin{multicols}{2}}
    
\item $\displaystyle\int_3^{\infty}\frac 1{(x-2)^2}\, dx$
\answer{
convergent
}

\item $\displaystyle\int_5^{\infty}\frac 1{x-4}\, dx$
\answer{
divergent
}

\item $\displaystyle\int_{-\infty}^0 x^3\, e^{-x^4}\, dx$
\answer{
convergent
}

\item $\displaystyle\int_{-\infty}^{\infty}\,\frac x{x^4+16}\, dx$
\answer{
convergent
}

\item $\displaystyle\int_{-\infty}^{0}\,\frac  1{x^2-4x+3}\, dx$
\answer{
convergent
}

\item $\displaystyle\int_{0}^{5}\,\frac  1{\sqrt{5-x}}\, dx$
\answer{
convergent
}

\item $\displaystyle\int_{1}^{2}\,\frac  1{(x-1)^{2/3}}\, dx$
\answer{
convergent
}

\item $\displaystyle\int_{0}^{2}\,\frac  1{x^2-4x+3}\, dx$
\answer{
divergent
}

\item $\displaystyle\int_{1}^{e}\,\frac  1{x\, (\ln x)^2}\, dx$
\answer{
divergent
}

\item $\displaystyle\int_{0}^{\pi/2}\,\tan^2x\, dx$
\answer{
divergent
}

\addtoanswerkey{\end{multicols}}
\end{problemblock}

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