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

question 23

Short Answer

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:

Associative Play

A stage of play in early childhood where children play together, engaging in similar activities or sharing materials without having a formal organization or goals.

Intrinsic Motivation

The drive to engage in activities for the inherent satisfaction or pleasure derived from the activity itself, rather than for some separable consequence.

Mildred Parten

An American sociologist known for her work on the social development of children and her study on children's play.

Extrinsic

Originating from outside, not inherent or intrinsic; often used to describe external motivations or rewards.