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+\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}