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I ain't got no limits' check-in

Check-in instructions

Make an educated guess on the value of the limit, in case it exists, by evaluating the function below at the points specified:

\lim_{x \to 2} \frac{x^2 - 2x}{x^2 -x-2}

x	2.5	2.1	2.01	2.001	1.999	1.99	1.9	1.5
f(x)

For the function $f$ whose graph is given below, state the value of each limit, in case it exists. If it does not exist, explain why.

$\displaystyle \lim_{x \to 1} f(x)$
$\displaystyle \lim_{x \to 3^-} f(x)$
$\displaystyle \lim_{x \to 3^+} f(x)$
$\displaystyle \lim_{x \to 3} f(x)$
$f(3)$

Sketch the graph of a function $f$ that satisfies all the following given conditions:

\displaystyle \lim_{x \to 3^+} f(x) = 4

\displaystyle \lim_{x \to 3^-} f(x) = 2

\displaystyle \lim_{x \to -2} f(x) = 2

f(-2) = 1

f(3) = 3