# What is the arc length of #r(t)=(t,t,t)# on #tin [1,2]#?

#sqrt(3) #

We seek the arc length of the vector function:

Which we can readily evaluated using:

Thus we gain the arc length:

This trivial result should come as no surprise as the given original equation is that of a straight line.

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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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- How do you find parametric equations for the tangent line to the curve with the given parametric equations at the specified point #x = 1+10 * sqrt(t)#, #y = t^5 - t#, and #z=t^5 + t# ; (11 , 0 , 2)?
- What is the arc length of the curve given by #r(t)= (ln(1/t),t^2,t)# on # t in [1, 10]#?

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