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

question 82

Essay

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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Definitions:

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