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Rewrite the following equation so that it equals zero on one side: [tex]\[ 2^2 - 4 = 5^{-} - 2 \][/tex]
Follow these steps for the first iteration:
\begin{tabular}{|c|c|} \hline Step 1 & \begin{tabular}{l} Rewrite the equation so that it equals zero on one side. \\ [tex]\[ (2^2 - 4) - (3^{-} - 2) = 0 \][/tex] \end{tabular} \\ \hline Step 2 & \begin{tabular}{l} Evaluate the rewritten equation at the lower and upper bounds. \\ To find the solution that lies between 1 and 2, set these values \\ as the lower and upper bounds while finding the root twice. \\ [tex]\[ (2^{1} - 4) - (3^{-1} - 2) \approx -0.333 \][/tex] \\ [tex]\[ (2^{2} - 4) - (3^{-1} - 2) \approx 1.889 \][/tex] \end{tabular} \\ \hline Step 3 & \begin{tabular}{l} Take the average of the lower and upper bounds. \\ [tex]\[ \frac{1+2}{2} = \frac{3}{2} \][/tex] \end{tabular} \\ \hline Step 4 & \begin{tabular}{l} Evaluate the rewritten equation at [tex]\( x = \frac{3}{2} \)[/tex]. \\ [tex]\[ (2(\frac{3}{2}) - 4) - (3(\frac{1}{2}) - 2) \approx 0.636 \][/tex] \end{tabular} \\ \hline Step 5 & \begin{tabular}{l} Since this value is positive, replace the previous lower bound so that \\ the bounds are now [tex]\( x = \frac{1}{2} \)[/tex] and [tex]\( x = 2 \)[/tex]. \end{tabular} \\ \hline \end{tabular}
Where did Jacob make a mistake and what was the error?
Sagot :
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