Use the Table of Values of F to Estimate the Limit

question 67

Multiple Choice

Use the table of values of f to estimate the limit.
- $\text { Let } f(x) =\frac{x+5}{x^{2}+7 x+10} \text {, find } \lim _{x \rightarrow 5} f(x)$

$\begin{array}{c|l|l|l|l|l|l}\mathrm{x} & -5.1 & -5.01 & -5.001 & -4.999 & -4.99 & -4.9 \\\hline \mathrm{f}(\mathrm{x}) & & & & & &\end{array}$

• A)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & -5.1 & -5.01 & -5.001 & -4.999 & -4.99 & -4.9 \\
• \hline \mathrm{f}(\mathrm{x}) & -0.4226 & -0.4322 & -0.4332 & -0.4334 & -0.4344 & -0.4448
• \end{array} \text {; limit }=-0.4333\)
• B)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & -5.1 & -5.01 & -5.001 & -4.999 & -4.99 & -4.9 \\
• \hline \mathrm{f}(\mathrm{x}) & -0.2226 & -0.2322 & -0.2332 & -0.2334 & -0.2344 & -0.2448
• \end{array} \text {; limit }=-0.2333\)
• C)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & -5.1 & -5.01 & -5.001 & -4.999 & -4.99 & -4.9 \\
• \hline \mathrm{f}(\mathrm{x}) & 0.3226 & 0.3322 & 0.3332 & 0.3334 & 0.3344 & 0.3448
• \end{array} \text {; limit }=0.3333\)
• D)
• \(\begin{array}{c|cccccc}
• \mathrm{x} & -5.1 & -5.01 & -5.001 & -4.999 & -4.99 & -4.9 \\
• \hline \mathrm{f}(\mathrm{x}) & -0.3226 & -0.3322 & -0.3332 & -0.3334 & -0.3344 & -0.3448
• \end{array} \text { limit }=-0.3333\)

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Definitions:

Type I Error

An error that occurs in hypothesis testing when a true null hypothesis is incorrectly rejected.

Type II Error

Occurs when a false null hypothesis is not rejected, meaning a real effect or difference is missed in a study or test.

Null Hypothesis

A default hypothesis that there is no significant difference or effect, typically to be tested against an alternative hypothesis.

Acquitting

The legal act of freeing an individual from a charge of an offence by a verdict of not guilty.