# Circle A has a center at #(5 ,-2 )# and a radius of #2 #. Circle B has a center at #(1 ,-4 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?

no overlap, smallest distance ≈ 1.47 units

• If sum of radii > d, then circles overlap

• If sum of radii < d, then no overlap

The 2 points here are (5 ,-2) and (1 ,-4)

sum of radii = radius of A + radius of B = 2 + 1 = 3

Since sum of radii < d, then no overlap of circles

smallest distance between circles = d - sum of radii

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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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