# How do you find the points of horizontal tangency of #r=asinthetacos^2theta#?

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To find the points of horizontal tangency for the polar curve ( r = a \sin(\theta) \cos^2(\theta) ), you need to find where the derivative of ( r ) with respect to ( \theta ) is zero and the second derivative is negative.

- Find the first derivative of ( r ) with respect to ( \theta ).
- Set the first derivative equal to zero and solve for ( \theta ).
- Check the second derivative of ( r ) with respect to ( \theta ) to ensure concavity.
- Evaluate ( r ) at the found ( \theta ) values to get the corresponding points of horizontal tangency.

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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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