# Circle A has a center at #(3 ,1 )# and a radius of #1 #. Circle B has a center at #(-2 ,1 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?

no overlap. distance = 1 unit.

The first step is to calculate the distance between the centres.

Here both centres have a y-coord = 1 , hence the line joining the centres is parallel to the x-axis

and it's length = 3 - (-2) = 3+ 2 = 5

now radius of A + radius of B = 1 + 3 = 4 which is < 5

hence there is no overlap.

distance between them = 5 - 4 = 1

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The circles do not overlap. The smallest distance between them is 2 units.

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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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