Use the Table of Values of F to Estimate the Limit

question 2

Multiple Choice

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

• A)
• \(\begin{array}{r|llllll}
• \mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 3.97484 & 3.99750 & 3.99975 & 4.00025 & 4.00250 & 4.02485
• \end{array} \text {; limit = 4.0 }\)
• B)
• \(\begin{array}{c|llllll}
• \mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 1.19245 & 1.19925 & 1.19993 & 1.20007 & 1.20075 & 1.20745
• \end{array} \text {; limit }=1.20\)
• 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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