Calculate the Average Rate of Change of the Given Function $[ a , a + h ]$

question 90

Multiple Choice

Calculate the average rate of change of the given function f over the interval $[ a , a + h ]$ , where $h = 1,0.1,0.01,0.001$ , and $0.0001$ . (It will be easier to do this if you first simplify the difference quotient (dq) as much as possible.) $f ( x ) = 5 x ^ { 2 } ; a = 0$ Complete the table. $$\begin{array} { | c | c | } \hline \boldsymbol { h } & d q \\\hline 1 & \\\hline 0.1 & \\\hline 0.01 & \\\hline 0.001 & \\\hline 0.0001 & \\\hline\end{array}$$

• A)\(\begin{array} { l }
• d q \\
• 5 \\
• 0.05 \\
• 0.0005 \\
• 0.000005 \\
• 0.00000005
• \end{array}\)
• B)\(\begin{array} { l }
• d q \\
• 5 \\
• 0.5 \\
• 0.05 \\
• 0.000001 \\
• 0.0001
• \end{array}\)
• C)\(\begin{array} { l }
• d q \\
• 6 \\
• 5.1 \\
• 5.01 \\
• 5.001 \\
• 5.0001
• \end{array}\)
• D)\(\begin{array} { l }
• d q \\
• 5 \\
• 0.5 \\
• 0.05 \\
• 0.005 \\
• 0.0005
• \end{array}\)

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Definitions:

Somatosensory Cortex

A part of the brain located in the parietal lobe that processes sensory information such as touch, temperature, and pain from various parts of the body.

A-Delta Fiber

A type of nerve fiber that is thinly myelinated and transmits pain and temperature sensations rapidly to the central nervous system.

Skin Sense Receptors

Skin sense receptors are specialized cells in the skin that detect and respond to various stimuli such as touch, temperature, and pain.

Temperature Detection

The physiological and neural processes allowing organisms to sense and respond to changes in ambient temperature.