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

Answer 1

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Answer 2

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

  1. Plot points by substituting various values of θ into the equation and calculating corresponding values of r.
  2. Connect the plotted points to form the graph of the polar equation.
  3. To find the tangents at the pole, differentiate the equation with respect to θ to obtain dr/dθ.
  4. Evaluate dr/dθ at θ = π/2 (since the pole corresponds to θ = π/2).
  5. Substitute θ = π/2 into the original equation to find r.
  6. 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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Answer from HIX Tutor

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.

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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