For Each of the Following Functions, Determine If the Graph $f(x)=4^{-x} \cos 3 x$

question 6

Essay

For each of the following functions, determine if the graph shows damped oscillation. If so, state the damping factor.
(a) $f(x)=4^{-x} \cos 3 x$
(b) $f(x)=x+\cos x$
(c) $f(x)=-5 x \cos 3 x$
(d) $f(x)=4 \sin \frac{x}{3}$
(e) $F(x)=0.45 e^{-0.1 x} \cos 2 x$

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Definitions:

Reticular Activating System

A network of neurons in the brainstem that regulates wakefulness and sleep-wake transitions.

Sedatives

Drugs that have a calming effect, reduce nervousness, and help induce sleep by depressing the central nervous system.

Central Nervous System Stimulant

A class of drugs that increase brain activity, leading to increased alertness, attention, and energy.

Delta-Wave

A type of high amplitude brain wave that is associated with deep sleep and is found in the human EEG (electroencephalogram).