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Question

# Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Then analyze the graph of the function. $g(x)=2^{-x^{2} / 2} \cos x$

Solution

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In the text function is given as:

$g(x)=2^{-\frac{x^2}{2}}\cos x$

This function can be written as product of two functions

\begin{align*} g(x)&=f(x)\cdot h(x)\\[1em] f(x)&=2^{-\frac{x^2}{2}}\\[1em] h(x)&=\cos(x) \end{align*}

Domain of both function is $x\in\lt-\infty, \infty \gt$.

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