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+\sethandouttitle{The Exponential and Logarithm Functions}
+
+
+\begin{enumerate}
+
+ \item Evaluate $f(x) = x^2$ and $g(x) = 2^x$ at $x=-3,-2,-1,0,1,2,3,4,5$. Graph both functions on the same graph.
+
+ \item Find the domain of $\displaystyle f(x) = \frac{ 1 - e^{x^2} }{ 1 - e^{1-x^2} }$ and $\displaystyle g(x) = \frac{ 1+x }{ e^{\cos x} }$.
+
+ \item Find the limit.
+ \begin{enumerate}
+ \item $\displaystyle\lim_{ x \rightarrow \infty } (1.0001)^x $.
+ \item $\displaystyle\lim_{x \rightarrow \infty} \frac{ e^{3x} - e^{-3x} }{ e^{3x} + e^{-3x} }$.
+ \item $\displaystyle \lim_{x \rightarrow \infty} ( e^{-2x} \cos x)$.
+ \end{enumerate}
+
+ \item Is $g(x) = 1/x$ one-to-one?
+
+ \item If $g(x) = 3 +x + e^x$, find $g^{-1}(4)$.
+
+ \newpage
+
+ \item The formula $C = \frac{5}{9}(F-32)$ expresses Celsius $C$ as a function of Fahrenheit $F$.
+ Find a formula for the inverse function and interpret it.
+
+ \item Find the inverse of the function $f(x) = 1 + \sqrt{ 2 + 3x }$.
+
+ \item Find the inverse of the function $f(x) = e^{2x-1}$.
+
+ \item Find $ (f^{-1})'(a)$ using the inverse derivative formula.
+ \begin{enumerate}
+ \item $f(x) = x^3$.
+ \item $f(x) = 9-x^2$.
+ \end{enumerate}
+ Then, find the inverse function first and differentiate it. Do your answers agree?
+
+
+ \item Find the exact value of each expression (without a calculator).
+ \begin{enumerate}
+ \item $\log_5(125)$.
+ \item $\displaystyle \log_3\left( \frac{1}{27} \right)$.
+ \item $\log_2 6 - \log_2 15 + \log_2 20$.
+ \end{enumerate}
+
+ \item Solve for $x$:
+ \begin{enumerate}
+ \item $e^{7-4x}=6$.
+ \item $\ln(3x-10) = 2$.
+ \item $\ln x + \ln (x-1) = 1$.
+ \end{enumerate}
+
+\end{enumerate}
+
+
+