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utf04-001
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 \( f(x) = \begin{cases} \sqrt{x} & \text{if } x\geq 0 \\ x^2 & \text{if } x<2 \end{cases} \)
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 $L$.
(This item has tags, notes and comments.)
utf04-002
Merged with [[
utf04-001
]]. . . .
1K - last updated 2009-08-20 23:05 by
EricHsu