How do you find the maximum value of #f(x)=20e^(-2x)*sin(3x) #?

Answer 1

The maximum value of #f(x)# is infinity.

Let #f(x)=20e^(-2x)sin3x#.
In order to find the maximum value of #f(x)#, we need to consider the functions which make up #f# and their maximum values. #f# is a product of #3# functions: #20#, #e^(-2x)# and #sin3x#. So the maximum of #f# will be the product of the maximum of these three functions.

It is also important to note that all three of these functions can take their max values simultaneously.

So the max value of #f# is #20*oo*1=oo#
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Answer 2

To find the maximum value of the function ( f(x) = 20e^{-2x} \cdot \sin(3x) ), you need to find the critical points by taking the derivative of the function, setting it equal to zero, and solving for ( x ). Then, you evaluate the second derivative to determine whether each critical point is a maximum, minimum, or inflection point. However, the function ( f(x) = 20e^{-2x} \cdot \sin(3x) ) does not have a maximum value as it increases without bound as ( x ) approaches infinity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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