Use the Table of Values of F to Estimate the Limit

question 181

Multiple Choice

Use the table of values of f to estimate the limit.
- $\text { Let } f(x) =\frac{x^{2}-4 x-5}{x^{2}-7 x+10} \text {, find } \lim _{x \rightarrow 5} f(x) \text {. }$
$\begin{array}{c|l|l|l|l|l|l}\mathrm{x} & 4.9 & 4.99 & 4.999 & 5.001 & 5.01 & 5.1 \\\hline \mathrm{f}(\mathrm{x}) & & & & & &\end{array}$

• A)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & 4.9 & 4.99 & 4.999 & 5.001 & 5.01 & 5.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 2.1345 & 2.1033 & 2.1003 & 2.0997 & 2.0967 & 2.0677
• \end{array} \text { limit }=2.1\)
• B)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & 4.9 & 4.99 & 4.999 & 5.001 & 5.01 & 5.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 1.9345 & 1.9033 & 1.9003 & 1.8997 & 1.8967 & 1.8677
• \end{array} \text { limit = } 1.9\)
• C)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & 4.9 & 4.99 & 4.999 & 5.001 & 5.01 & 5.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 2.0345 & 2.0033 & 2.0003 & 1.9997 & 1.9967 & 1.9677
• \end{array} \text { limit = 2 }\)
• D)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & 4.9 & 4.99 & 4.999 & 5.001 & 5.01 & 5.1 \\
• \hline \mathrm{f}(\mathrm{x}) & 0.5775 & 0.5720 & 0.5715 & 0.5714 & 0.5708 & 0.5652
• \end{array} \text { limit }=0.5714\)

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Definitions:

Secured Bonds

Bonds that are backed by collateral, such as real estate or other assets, to reduce the risk of default to investors.

Bond Principal

The face value of a bond, or the amount of money the bond issuer will pay back to the bondholder at maturity.

Serial Bonds

Bonds that are issued under the same contract but mature at different times, allowing the issuer to spread the repayment over several periods.

Principal Retirement

The act of paying off the original sum of money borrowed in a loan, excluding interest payments.