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:

Pituitary Gland

A small, pea-sized gland located at the base of the brain, called the "master gland" because it produces hormones that control other glands and many body functions including growth.

Synaptic Terminals

The ends of axons where neurotransmitters are released to transmit signals across synapses to other neurons or muscle cells.

Neurotransmitter

Chemical substances in the brain that transmit signals from one neuron to another, playing a major role in shaping everyday functions and mood.

Excitatory

Referring to substances or signals that increase the activity of the brain or other body systems, potentially leading to heightened arousal or action.