What is the arclength between two points on a curve? How does it differ from the distance?

Answer 1

The distance is the arc length on a straight line. The arc length is the distance along the arc.

Example

For the points #(-1,0)# and #(1,0)#,
the distance between the points (the length of the straight line joining them) is #2#.
The length of the arc on the unit circle: #x^2+y^2=1# is half the circumference, so it is #pi#. (More completely, the lengths of both the upper and lower arcs are #pi#.)
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Answer 2

The arclength between two points on a curve is the length of the curve that connects the two points. It is a measure of how long the curve is between those two points.

Distance, on the other hand, is the shortest path between two points, which is typically a straight line. The arclength considers the actual path of the curve, while the distance is a straight-line measurement.

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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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