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Evaluate the Function f(x)=7(x2x2)f ( x ) = 7 \left( \frac { \sqrt { x } - \sqrt { 2 } } { x - 2 } \right)

Question 34

Short Answer

Evaluate the function f(x)=7(x2x2)f ( x ) = 7 \left( \frac { \sqrt { x } - \sqrt { 2 } } { x - 2 } \right)
at the given numbers (correct to six decimal places). Use the results to guess the value of the limit limx2f(x)\lim _ { x \rightarrow 2 } f ( x ) .
xf(x)1.61.81.91.991.9992.42.22.12.012.001 Limit \begin{array}{|c|c|}\hline x & f(x) \\\hline 1.6 & \\\hline 1.8 & \\\hline 1.9 & \\\hline 1.99 & \\\hline 1.999 & \\\hline 2.4 & \\\hline 2.2 & \\\hline 2.1 & \\\hline 2.01 & \\\hline 2.001 & \\\hline \text { Limit } & \\\hline\end{array}

Correct Answer:

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\[\begin{array} { l }
2.61279...

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