# Circle A has a center at #(9 ,4 )# and a radius of #4 #. Circle B has a center at #(-2 ,6 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

no overlap, smallest distance ≈ 2.18

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

The 2 points here are (9 ,4) and (-2 ,6)

Sum of radii = radius of A + radius of B = 4 + 5 = 9

Since sum of radii < d , then no overlap

smallest distance between them = d - sum of radii

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No, the circles do not overlap. The smallest distance between them is 6.

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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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