# What is the arclength of #(t-3,t+4)# on #t in [2,4]#?

The formula for parametric arc length is:

We begin by finding the two derivatives:

This gives that the arc length is:

In fact, since the parametric function is so simple (it is a straight line), we don't even need the integral formula. If we plot the function in a graph, we can just use the regular distance formula:

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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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