Use the Table of Values of F to Estimate the Limit

question 115

Multiple Choice

Use the table of values of f to estimate the limit.
- $\text { Let } f(x) =x^{2}-5 \text {, find } \lim _{x \rightarrow \theta} f(x)$
$\begin{array}{c|c|c|c|c|c|c}\mathrm{x} & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\\hline \mathrm{f}(\mathrm{x}) & & & & & &\end{array}$

• A)
• \(\begin{array}{c|llllcc}
• \mathrm{x} & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\
• \mathrm{f}(\mathrm{x}) & -2.9910 & -2.9999 & -3.0000 & -3.0000 & -2.9999 & -2.9910
• \end{array} ; \text { limit }=-3.0\)
• B)
• \(\begin{array}{r|llllll}
• \mathrm{x} & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\
• \hline \mathrm{f}(\mathrm{x}) & -1.4970 & -1.4999 & -1.5000 & -1.5000 & -1.4999 & -1.4970
• \end{array} \text {; limit }=-15.0\)
• C)
• \(\begin{array}{c|llllll}
• \mathrm{x} & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\
• \hline \mathrm{f}(\mathrm{x}) & -1.4970 & -1.4999 & -1.5000 & -1.5000 & -1.4999 & -1.4970
• \end{array} \text { limit }=\infty\)
• D)
• \(\begin{array}{c|llllll}
• \mathrm{x} & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\
• \hline \mathrm{f}(\mathrm{x}) & -4.9900 & -4.9999 & -5.0000 & -5.0000 & -4.9999 & -4.9900
• \end{array} \text {; limit }=-5.0\)

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Definitions:

Short-Run

A period of time during which at least one input, such as plant size, cannot be changed; contrasts with the long-run where all inputs are variable.

Marginal Cost

Marginal cost is the additional cost incurred from producing one extra unit of a good or service, an important concept in economics for determining optimal production levels.

Average Total Cost

The total cost of production (fixed and variable costs combined) divided by the quantity of output, a key factor in pricing and profitability analyses.

Marginal Revenue

The additional income generated from selling one more unit of a product or service.