Question

compute the values of \\(f(x) = \frac{x - 7}{(x - 1)^2}\\) in the table to the right and use them to determine \\(\lim_{x \to 1} f(x)\\).

complete the table below.

\\(\

$$\begin{array}{|c|c|c|c|} \\hline x & f(x) & x & f(x) \\\\ \\hline 1.1 & -590 & 0.9 & -610 \\\\ \\hline 1.01 & -59900 & 0.99 & -60100 \\\\ \\hline 1.001 & -5999000 & 0.999 & -6001000 \\\\ \\hline 1.0001 & -599990000 & 0.9999 & -600010000 \\\\ \\hline \\end{array}$$

\\)
(type integers or decimals.)

determine \\(\lim_{x \to 1} f(x)\\) using these table values.

\\(\lim_{x \to 1} f(x) = \square\\) (simplify your answer.)

Explanation:

Analyze the table values as \(x \to 1\)

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Determine the limit using analytical evaluation

$$ \lim_{x \to 1} \frac{x - 7}{(x - 1)^2} = \frac{1 - 7}{0^+} = \frac{-6}{0^+} = -\infty $$

Answer:

Determine \(\lim_{x \to 1} f(x)\) using these table values.

\(\lim_{x \to 1} f(x) =\) <blank>\(-\infty\)</blank>