utf04-001

1. Fill in the tables, (use calculators if necessary) then guess what the {last} two boxes should be.
   
   

   $\frac{1}{x^2}$

   $\dots$

   ???

   $x$

   $-1$

   $\frac{1}{2}$

   $-\frac{1}{4}$

   $\frac{1}{9}$

   $-\frac{1}{16}$

   $\frac{1}{25}$

   $\frac{1}{1000}$

   $ -\frac{3}{10^6}$

   $-\frac{1}{10^{15}}$

   $\frac{1}{10^{15}}$

   $-\frac{1}{10^{20}}$

   $\dots$

   ???

   
   
   

   $x \sin \frac{2\pi}{x}$

   $\dots$

   ???

   $x$

   $-4$

   $4$

   $-\frac{4}{301}$

   $-\frac{4}{401}$

   $\frac{4}{3}$

   $\frac{4}{5}$

   $\frac{4}{7}$

   $ \frac{4}{201}$

   $\frac{4}{301}$

   $\frac{4}{2001}$

   $\frac{4}{3001}$

   $\dots$

   ???

   
   
   

   $f(x)$

   $\dots$

   ???

   $x$

   $-1$

   $1$

   $-0.1$

   $0.1$

   $-0.01$

   $0.01$

   $10^{-3}$

   $ -10^{-3}$

   $-10^{-4}$

   $10^{-4}$

   $10^{-5}$

   $\dots$

   ???

   where \( f(x) = \begin{cases} \sqrt{x} & \text{if } x\geq 0 \\ x^2 & \text{if } x<2 \end{cases} \)
2. 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 $L$.

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

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Table restored.

• Eric Hsu 2008-07-10