9bf4bf…: “Aboard a loud angle”

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Complete the following table using exact values.

$\begin {array}{|c|c|c|c|c|c|c|c|c|} \hline x & \frac {1}{3} & \frac {1}{30} & \frac {1}{300} & \frac {1}{301} & \frac {1}{1000} & \frac {1}{1001} & \frac {1}{50000} & \frac {1}{100004}\\\hline \frac {1}{x} & \answer {3} & \answer {30} & \answer {300} & \answer {301} & \answer {1000} & \answer {1001} & \answer {50000} & \answer {100004} \\\hline \end {array}$

Based on the table above, make a conjecture about $\lim _{x\to 0^{+}}\frac {1}{x}$ . Does it exist? Explain.

It seems like the limit does not exist. The values $\frac {1}{x}$ don’t seem to approach any number, even when $x$ is very close to 0. It seems that these values just grow and grow and keep growing.

Based only on the table of values, can you determine for certain if the limit exists or not?

Do you need to use a limit to determine the behavior of $f(x)$ at $x=0$ ?

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ctrl+backspace	Delete current entry in list or column in matrix
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