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)
• \(\begin{array}{c|llllll}
• \mathrm{x} & 3.9 & 3.99 & 3.999 & 4.001 & 4.01 & 4.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 5.07736 & 5.09775 & 5.09978 & 5.10022 & 5.10225 & 5.12236
• \end{array} \text { limit = 5.10 }\)

---

Definitions:

Battlefield Performance

The effectiveness, strategy, and outcomes of military units engaged in combat during a conflict.

Fifty-Fourth Massachusetts

An African American regiment during the American Civil War, celebrated for its bravery and as a symbol of black soldiers' contributions to the Union victory.

Fort Wagner

A site of significant battle during the American Civil War, particularly known for the valiant charge of the 54th Massachusetts Volunteer Infantry, an African American regiment, in 1863.

Jefferson Davis

The President of the Confederate States of America during the American Civil War, known for his leadership in the secessionist movement and efforts to establish a separate nationhood for the southern states.