How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3sintheta#?
graph{x^2+y^2=3y [5, 5, 1, 4]}
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To sketch the graph of the polar equation ( r = 3\sin(\theta) ) and find the tangents at the pole, follow these steps:

Sketching the Graph:
 Plot points for different values of θ, such as 0°, 30°, 45°, 90°, etc.
 Substitute each θ value into the equation ( r = 3\sin(\theta) ) to find the corresponding value of r.
 Plot these points on polar coordinates (r, θ).
 Connect the points to form the graph of the polar equation.

Finding Tangents at the Pole:
 At the pole (θ = 0° or θ = 180°), the equation ( r = 3\sin(\theta) ) becomes ( r = 0 ).
 When ( r = 0 ), it implies that the curve touches the pole.
 To find the tangent at the pole, calculate the derivative ( \frac{dr}{d\theta} ) and evaluate it at θ = 0° or θ = 180°.
 The tangent line at the pole is perpendicular to the radius vector. So, find the slope of the tangent line and then use it to write the equation of the tangent line.
 Use the equation of the tangent line to sketch it on the graph.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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