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\title{Calculus and Elements of Linear Algebra I}
\author{Homework 2}
\date{Due on Moodle, September 21, 2020}
\maketitle

\begin{enumerate}

\item Draw the graphs of the following equations in two variables $x$
and $y$. 
\begin{enumerate}
\item $\displaystyle 3\,x-2\,y=6$
\item $\displaystyle y=5$
\item $\displaystyle (y-2)^2 = 2 \, (x+1)$
\item $(x-1)^2+(y-1)^2 = 4$
\end{enumerate}

\item For each of the examples from Question~1, determine whether it is
the graph of a function $y=f(x)$.  If so, find $f(x)$, its domain, and
its range.

\item For each of the examples from Question~1, determine whether it is
the graph of a function $x = g(y)$.  If so, find $g(y)$, its domain,
and its range.

\item Let
\[
  f(x) = 5^{x-2} \,.
\]
Find the inverse function of $f$, denoted $f^{-1}$, and state domain
and range of $f$ and $f^{-1}$.\footnote{Note that $f^{-1}$ is common
symbolic notation for the inverse function.  It does \emph{not} denote
the function $1/f(x)$!}


\item Compute the following limits.
\begin{enumerate}
\item $\displaystyle \lim_{x \to 4} x^2+5 \, x - 5$
\item $\displaystyle \lim_{s \to 3} \frac{s^2-9}{s-3}$
\item $\displaystyle \lim_{t \to 0} \frac{t^2}t$
\item $\displaystyle \lim_{w \to 3} \frac{\dfrac1w-\dfrac13}{w-3}$
\item $\displaystyle \lim_{h \to 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{x}$
\end{enumerate}





\end{enumerate}

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