Evaluate the Function $f(x)=7\left(\frac{\sqrt{x}-\sqrt{2}}{x-2}\right)$ At the Given Numbers (Correct to Six Decimal Places)

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

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2.612794,2.540047,2.506608,2....

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