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diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-1.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-1.tex new file mode 100644 index 0000000000..3e04869607 --- /dev/null +++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-1.tex @@ -0,0 +1,44 @@ +\sethandouttitle{From First Principles} + + + +\allhandoutinfo{} + +\begin{enumerate} + \item Find the equation of the tangent line to the curves + \begin{enumerate} + \item $y=4x-3x^2$ ar $(2,-4)$. + \vfill + \item $y = \sqrt{x}$ at $(1,1)$. + \vfill + \end{enumerate} + + \item The displacement of a particle moving in a straight line is given by the equation of motion $s=1/t^2$. + Find the velocity of the particle at $t=a$, $t=1$, $t=2$ and $t=3$. + + \vfill + \newpage + + \item Each limit represents the derivative of some function $f$ at a number $a$. State such an $f$ and $a$ in each case. + \begin{enumerate} + \item $\displaystyle\lim_{h \rightarrow 0} \frac{ (1+h)^8 - 1 }{h}$. + \vfill + \item $\displaystyle\lim_{x \rightarrow 5} \frac{ 2^x - 32}{x-5}$. + \vfill + \item $\displaystyle\lim_{h \rightarrow 0} \frac{ \cos(\pi + h) + 1 }{h}$. + \vfill + \end{enumerate} + + \newpage + \item The cost in dollars of producing $x$ units of a certain commodity is $C(x)= 500 + 10x + 0.05 x^2$. + \begin{enumerate} + \item Find the average rate of change of $C$ with respect to $x$ when the production level is changed + from $x=100$ to $x=105$. + \vfill + \item Find the average rate of change of $C$ with respect to $x$ when the production level is changed + from $x=100$ to $x=101$. + \vfill + \item Find the instantaneous rate of change of $C$ with respect to $x$ when $x=100$. + \vfill + \end{enumerate} +\end{enumerate} |