Use a graphing utility to graph the function and the damping factor of the function in the same viewing window.
f(x) = e−3x sin(x)

analyze the graph of the function using the method in example 6. (enter your answers as a comma-separated list. use n to represent an arbitrary integer if necessary.)
y = ±e−3x touches y = e−3x sin(x) at:

y = e−3x sin(x) has x-intercepts at:

The function touches the damping factor

at x= and x=

The x-intercept of f(x) is

at x=

Step-by-step explanation:

Given function is f(x)= and damping factor as y= and y=

To find when function touches the damping factor:

For f(x)= and y=

Equating the both the equation,

x=

For f(x)= and y=

Equating the both the equation,

x=

Therefore, The function touches the damping factor x= and x=

To find x-intercept of f(x):

For x-intercept, y=0

f(x)=

y=

Hence, is always greater than zero.

Therefore,

x=

Thus,

The x-intercept of f(x) is at x=

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answer