# For #f(x)=xsin^3(x/3)# what is the equation of the tangent line at #x=pi#?

You have to find the derivative:

In this case, the derivative of the trigonometric function is actually a combination of 3 elementary functions. These are:

The way this will be solved is as follows:

Therefore:

The derivation of the tangent equation:

Substituting the following values:

Therefore, the equation becomes:

graph{x(sin(x/3))^3 [-1.53, 9.57, -0.373, 5.176]}

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The equation of the tangent line at x=pi for the function f(x)=xsin^3(x/3) is y = -pi/3 + 3pi/2.

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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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