Problems DB: utf04-001

$\begin{enumerate} \item Fill in the tables, (use calculators if necessary) then guess what the {\it last} two boxes should be. \renewcommand{\arraystretch}{1.5} \begin{tabular}{|c||c| c| c| c|c|c|c|c| c| c| c|c|c| } \hline $\frac{1}{x^2}$ & & & & & & & & & & & & $\dots$ & ??? \\ \hline $x$ &$-1$ &$\frac{1}{2}$ & $-\frac{1}{4}$ & $\frac{1}{9}$& $-\frac{1}{16}$ & $\frac{1}{25}$&$\frac{1}{1000}$ & $ -\frac{3}{10^6}$ & $-\frac{1}{10^{15}}$ &$\frac{1}{10^{15}}$ &$-\frac{1}{10^{20}}$ & $\dots$ & ???\\ \hline \end{tabular} \begin{tabular}{|c||c| c| c| c|c|c|c|c| c| c| c|c|c| } \hline $x \sin \frac{2\pi}{x}$ & & & & & & & & & & & & $\dots$ & ??? \\ \hline $x$ &$-4$ &$4$ & $-\frac{4}{301}$ & $-\frac{4}{401}$& $\frac{4}{3}$ & $\frac{4}{5}$&$\frac{4}{7}$ & $ \frac{4}{201}$ & $\frac{4}{301}$ &$\frac{4}{2001}$ &$\frac{4}{3001}$ & $\dots$ & ???\\ \hline \end{tabular} \begin{tabular}{|c||c| c| c| c|c|c|c|c| c| c| c|c|c| } \hline $f(x)$ & & & & & & & & & & & & $\dots$ & ??? \\ \hline $x$ &$-1$ &$1$ & $-0.1$ & $0.1$& $-0.01$ & $0.01$&$10^{-3}$ & $ -10^{-3}$ & $-10^{-4}$ &$10^{-4}$ &$10^{-5}$ & $\dots$ & ???\\ \hline \end{tabular} where $ f(x) = \begin{cases} \sqrt{x} & \mbox{if } x\geq 0 \\ x^2 & \mbox{if } x<2 \end{cases} $ \item For each of the tables in (1) write it as a limit; i.e. $\lim_{x\to a} f( x) = L $ where you fill in $ f( x)$, $a$, and $L$. \end{enumerate}$

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Tags: limits, trig, rational, using-notation,piecewise-defined, prediction, n--n, t1, c1 , restored

Table restored.

Eric Hsu 2008-07-10