Use the table of values of f to estimate the limit.
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\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}

\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

\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

\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

\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

Use the Slopes of UQ, UR, US, and UT to Estimate

Multiple Choice