# What is the slope of the tangent line of #r=-2sin(3theta)-12cos(theta/2)# at #theta=(-pi)/3#?

1) Differentiate both sides

2) Examine

3) Get that the slope is

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To find the slope of the tangent line of the polar curve r = -2sin(3θ) - 12cos(θ/2) at θ = -π/3, you would first find the derivative of r with respect to θ, then evaluate it at θ = -π/3 to get the slope of the tangent line at that point.

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To find the slope of the tangent line of ( r = -2\sin(3\theta) - 12\cos(\frac{\theta}{2}) ) at ( \theta = -\frac{\pi}{3} ), you first need to find the derivative ( \frac{dr}{d\theta} ). Then evaluate the derivative at ( \theta = -\frac{\pi}{3} ) to get the slope of the tangent line at that point.

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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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