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diff --git a/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-2-1.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-2-1.tex new file mode 100644 index 00000000000..4c03b10083e --- /dev/null +++ b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-2-1.tex @@ -0,0 +1,55 @@ +\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} + + + |