Use the Table of Values of F to Estimate the Limit

question 169

Multiple Choice

Use the table of values of f to estimate the limit.
- $\text { Let } f(x) =\frac{x-4}{\sqrt{x}-2} \text {, find } \lim _{x-4} f(x)$
$\begin{array}{c|l|l|l|l|l|l}\mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\\hline \mathrm{f}(\mathrm{x}) & & & & & &\end{array}$

• A)
• \(\begin{array}{c|llllll}
• \mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 3.97484 & 3.99750 & 3.99975 & 4.00025 & 4.00250 & 4.02485
• \end{array} \text {; limit = 4.0 }\)
• B)
• \(\begin{array}{c|llllll}
• \mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\
• \hline f(x) & 1.19245 & 1.19925 & 1.19993 & 1.20007 & 1.20075 & 1.20745
• \end{array} \text {; limit }=1.20\)
• C)
• \(\begin{array}{c|llllll}
• \mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 1.19245 & 1.19925 & 1.19993 & 1.20007 & 1.20075 & 1.20745
• \end{array} ; \text { limit }=\infty\)
• D)
• \(\begin{array}{c|llllll}
• \mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 5.07736 & 5.09775 & 5.09978 & 5.10022 & 5.10225 & 5.12236
• \end{array} \text { limit = 5.10 }\)

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Definitions:

Demand for Wine

The desire or need for wine that consumers are willing and able to purchase at various prices.

Cournot Duopolists

Two firms competing in the same market, where each chooses its quantity of output independently and simultaneously, anticipating the other's choice.

Imports

Goods or services brought into a country from abroad for sale.

Inverse Demand

A mathematical representation of demand that expresses price as a function of quantity demanded, typically showing how the price will adjust to achieve market equilibrium.