# How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3costheta#?

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To sketch the graph of the polar equation (r = 3\cos(\theta)) and find the tangents at the pole, follow these steps:

- Plot points by substituting various values of θ into the equation and calculating corresponding values of r.
- Connect the plotted points to form the graph of the polar equation.
- To find the tangents at the pole, differentiate the equation with respect to θ to obtain dr/dθ.
- Evaluate dr/dθ at θ = π/2 (since the pole corresponds to θ = π/2).
- Substitute θ = π/2 into the original equation to find r.
- Use the values of r and dr/dθ at θ = π/2 to determine the equations of the tangents at the pole.

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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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