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Suppose $f$ is a strictly decreasing function. This means that as $x$ increases, the values of $f(x)$ decrease. The table below shows several values of $f(x)$.

 x f(x) 1 15.2 2 13.9 3 Undefined 4 9.7 5 5.2

Using values from the table only, what would be the most accurate overestimate for $\displaystyle \lim _{x \to 3} f(x)$?

$1$ $2$ $3$ $4$ $5$ $15.2$ $13.9$ Undefined $9.7$ $5.2$ You need more information to determine the most accurate overestimate.

If you use $f(4)$ to approximate $\lim _{x \to 3} f(x)$, how large could the error be using this approximation?

$2$ $4$ $9.7$ $13.9 – 9.7$ $\frac {13.9-9.7}{2}$ Cannot be sure without more information
For which of the following does $\lim _{x \to a} f(x)$ exist?
 I II III IV IV only III and IV only II, III, and IV only I, II, III, and IV None of these
Which of the following most accurately represents the meaning of $\lim _{x \to a} f(x) = L$?
$L$ is equal to $f(a)$ $f(x)$ gets close to $L$ but never equals $L$ The process of getting closer and closer to $L$ $f(x)$ can become as close to $L$ as desired by making $x$ get closer to $a$ $x$ can become as close to $L$ as desired by making $f(x)$ get closer to $a$ $\lim f(x)$ is an approximation that you can make as close to $L$ as desired We can’t say for sure because $f(a)$ might be undefined