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

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

Example

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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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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.

- How do you solve #y'=(2x-3)/(y^2+y+4)# given y(1)=2?
- What is the arc length of #f(x)=sqrt(18-x^2) # on #x in [0,3]#?
- What is the solution to the Differential Equation #(d^2y)/(dx^2) - 6dy/dx = 54x + 18#?
- What is a general solution to the differential equation #1+y^2-y'sqrt(1-x^2)=0#?
- How do you find the arc length of the cardioid #r = 1+cos(theta)# from 0 to 2pi?

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