# How do you find the points of horizontal tangency of #r=2cos(3theta-2)#?

The slope, m, of a Tangent to a Polar Curve is found using the equation:

The point of is of tangency is:

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To find the points of horizontal tangency of the polar curve ( r = 2\cos(3\theta - 2) ), set the derivative of ( r ) with respect to ( \theta ) equal to zero and solve for ( \theta ). Then, plug these values of ( \theta ) back into the original equation to find the corresponding ( r ) values.

The derivative of ( r ) with respect to ( \theta ) is given by:

[ \frac{dr}{d\theta} = -2\sin(3\theta - 2) ]

Set this equal to zero and solve for ( \theta ):

[ -2\sin(3\theta - 2) = 0 ]

[ \sin(3\theta - 2) = 0 ]

[ 3\theta - 2 = k\pi ]

[ \theta = \frac{2}{3} + \frac{k\pi}{3} ]

where ( k ) is an integer.

Plug these values of ( \theta ) back into the original equation ( r = 2\cos(3\theta - 2) ) to find the corresponding ( r ) values. This will give you the 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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